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3302 lines
213 KiB
3302 lines
213 KiB
"""
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This code is automatically generated. Never edit it manually.
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For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
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"""
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from sympy.external import import_module
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matchpy = import_module("matchpy")
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if matchpy:
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from matchpy import Pattern, ReplacementRule, CustomConstraint, is_match
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from sympy.integrals.rubi.utility_function import (
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Int, Sum, Set, With, Module, Scan, MapAnd, FalseQ,
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ZeroQ, NegativeQ, NonzeroQ, FreeQ, NFreeQ, List, Log, PositiveQ,
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PositiveIntegerQ, NegativeIntegerQ, IntegerQ, IntegersQ,
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ComplexNumberQ, PureComplexNumberQ, RealNumericQ, PositiveOrZeroQ,
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NegativeOrZeroQ, FractionOrNegativeQ, NegQ, Equal, Unequal, IntPart,
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FracPart, RationalQ, ProductQ, SumQ, NonsumQ, Subst, First, Rest,
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SqrtNumberQ, SqrtNumberSumQ, LinearQ, Sqrt, ArcCosh, Coefficient,
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Denominator, Hypergeometric2F1, Not, Simplify, FractionalPart,
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IntegerPart, AppellF1, EllipticPi, EllipticE, EllipticF, ArcTan,
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ArcCot, ArcCoth, ArcTanh, ArcSin, ArcSinh, ArcCos, ArcCsc, ArcSec,
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ArcCsch, ArcSech, Sinh, Tanh, Cosh, Sech, Csch, Coth, LessEqual, Less,
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Greater, GreaterEqual, FractionQ, IntLinearcQ, Expand, IndependentQ,
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PowerQ, IntegerPowerQ, PositiveIntegerPowerQ, FractionalPowerQ, AtomQ,
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ExpQ, LogQ, Head, MemberQ, TrigQ, SinQ, CosQ, TanQ, CotQ, SecQ, CscQ,
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Sin, Cos, Tan, Cot, Sec, Csc, HyperbolicQ, SinhQ, CoshQ, TanhQ, CothQ,
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SechQ, CschQ, InverseTrigQ, SinCosQ, SinhCoshQ, LeafCount, Numerator,
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NumberQ, NumericQ, Length, ListQ, Im, Re, InverseHyperbolicQ,
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InverseFunctionQ, TrigHyperbolicFreeQ, InverseFunctionFreeQ, RealQ,
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EqQ, FractionalPowerFreeQ, ComplexFreeQ, PolynomialQ, FactorSquareFree,
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PowerOfLinearQ, Exponent, QuadraticQ, LinearPairQ, BinomialParts,
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TrinomialParts, PolyQ, EvenQ, OddQ, PerfectSquareQ, NiceSqrtAuxQ,
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NiceSqrtQ, Together, PosAux, PosQ, CoefficientList, ReplaceAll,
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ExpandLinearProduct, GCD, ContentFactor, NumericFactor,
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NonnumericFactors, MakeAssocList, GensymSubst, KernelSubst,
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ExpandExpression, Apart, SmartApart, MatchQ,
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PolynomialQuotientRemainder, FreeFactors, NonfreeFactors,
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RemoveContentAux, RemoveContent, FreeTerms, NonfreeTerms,
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ExpandAlgebraicFunction, CollectReciprocals, ExpandCleanup,
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AlgebraicFunctionQ, Coeff, LeadTerm, RemainingTerms, LeadFactor,
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RemainingFactors, LeadBase, LeadDegree, Numer, Denom, hypergeom, Expon,
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MergeMonomials, PolynomialDivide, BinomialQ, TrinomialQ,
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GeneralizedBinomialQ, GeneralizedTrinomialQ, FactorSquareFreeList,
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PerfectPowerTest, SquareFreeFactorTest, RationalFunctionQ,
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RationalFunctionFactors, NonrationalFunctionFactors, Reverse,
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RationalFunctionExponents, RationalFunctionExpand, ExpandIntegrand,
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SimplerQ, SimplerSqrtQ, SumSimplerQ, BinomialDegree, TrinomialDegree,
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CancelCommonFactors, SimplerIntegrandQ, GeneralizedBinomialDegree,
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GeneralizedBinomialParts, GeneralizedTrinomialDegree,
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GeneralizedTrinomialParts, MonomialQ, MonomialSumQ,
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MinimumMonomialExponent, MonomialExponent, LinearMatchQ,
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PowerOfLinearMatchQ, QuadraticMatchQ, CubicMatchQ, BinomialMatchQ,
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TrinomialMatchQ, GeneralizedBinomialMatchQ, GeneralizedTrinomialMatchQ,
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QuotientOfLinearsMatchQ, PolynomialTermQ, PolynomialTerms,
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NonpolynomialTerms, PseudoBinomialParts, NormalizePseudoBinomial,
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PseudoBinomialPairQ, PseudoBinomialQ, PolynomialGCD, PolyGCD,
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AlgebraicFunctionFactors, NonalgebraicFunctionFactors,
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QuotientOfLinearsP, QuotientOfLinearsParts, QuotientOfLinearsQ,
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Flatten, Sort, AbsurdNumberQ, AbsurdNumberFactors,
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NonabsurdNumberFactors, SumSimplerAuxQ, Prepend, Drop,
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CombineExponents, FactorInteger, FactorAbsurdNumber,
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SubstForInverseFunction, SubstForFractionalPower,
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SubstForFractionalPowerOfQuotientOfLinears,
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FractionalPowerOfQuotientOfLinears, SubstForFractionalPowerQ,
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SubstForFractionalPowerAuxQ, FractionalPowerOfSquareQ,
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FractionalPowerSubexpressionQ, Apply, FactorNumericGcd,
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MergeableFactorQ, MergeFactor, MergeFactors, TrigSimplifyQ,
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TrigSimplify, TrigSimplifyRecur, Order, FactorOrder, Smallest,
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OrderedQ, MinimumDegree, PositiveFactors, Sign, NonpositiveFactors,
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PolynomialInAuxQ, PolynomialInQ, ExponentInAux, ExponentIn,
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PolynomialInSubstAux, PolynomialInSubst, Distrib, DistributeDegree,
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FunctionOfPower, DivideDegreesOfFactors, MonomialFactor, FullSimplify,
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FunctionOfLinearSubst, FunctionOfLinear, NormalizeIntegrand,
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NormalizeIntegrandAux, NormalizeIntegrandFactor,
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NormalizeIntegrandFactorBase, NormalizeTogether,
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NormalizeLeadTermSigns, AbsorbMinusSign, NormalizeSumFactors,
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SignOfFactor, NormalizePowerOfLinear, SimplifyIntegrand, SimplifyTerm,
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TogetherSimplify, SmartSimplify, SubstForExpn, ExpandToSum, UnifySum,
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UnifyTerms, UnifyTerm, CalculusQ, FunctionOfInverseLinear,
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PureFunctionOfSinhQ, PureFunctionOfTanhQ, PureFunctionOfCoshQ,
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IntegerQuotientQ, OddQuotientQ, EvenQuotientQ, FindTrigFactor,
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FunctionOfSinhQ, FunctionOfCoshQ, OddHyperbolicPowerQ, FunctionOfTanhQ,
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FunctionOfTanhWeight, FunctionOfHyperbolicQ, SmartNumerator,
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SmartDenominator, SubstForAux, ActivateTrig, ExpandTrig, TrigExpand,
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SubstForTrig, SubstForHyperbolic, InertTrigFreeQ, LCM,
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SubstForFractionalPowerOfLinear, FractionalPowerOfLinear,
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InverseFunctionOfLinear, InertTrigQ, InertReciprocalQ, DeactivateTrig,
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FixInertTrigFunction, DeactivateTrigAux, PowerOfInertTrigSumQ,
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PiecewiseLinearQ, KnownTrigIntegrandQ, KnownSineIntegrandQ,
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KnownTangentIntegrandQ, KnownCotangentIntegrandQ,
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KnownSecantIntegrandQ, TryPureTanSubst, TryTanhSubst, TryPureTanhSubst,
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AbsurdNumberGCD, AbsurdNumberGCDList, ExpandTrigExpand,
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ExpandTrigReduce, ExpandTrigReduceAux, NormalizeTrig, TrigToExp,
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ExpandTrigToExp, TrigReduce, FunctionOfTrig, AlgebraicTrigFunctionQ,
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FunctionOfHyperbolic, FunctionOfQ, FunctionOfExpnQ, PureFunctionOfSinQ,
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PureFunctionOfCosQ, PureFunctionOfTanQ, PureFunctionOfCotQ,
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FunctionOfCosQ, FunctionOfSinQ, OddTrigPowerQ, FunctionOfTanQ,
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FunctionOfTanWeight, FunctionOfTrigQ, FunctionOfDensePolynomialsQ,
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FunctionOfLog, PowerVariableExpn, PowerVariableDegree,
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PowerVariableSubst, EulerIntegrandQ, FunctionOfSquareRootOfQuadratic,
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SquareRootOfQuadraticSubst, Divides, EasyDQ, ProductOfLinearPowersQ,
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Rt, NthRoot, AtomBaseQ, SumBaseQ, NegSumBaseQ, AllNegTermQ,
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SomeNegTermQ, TrigSquareQ, RtAux, TrigSquare, IntSum, IntTerm, Map2,
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ConstantFactor, SameQ, ReplacePart, CommonFactors,
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MostMainFactorPosition, FunctionOfExponentialQ, FunctionOfExponential,
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FunctionOfExponentialFunction, FunctionOfExponentialFunctionAux,
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FunctionOfExponentialTest, FunctionOfExponentialTestAux, stdev,
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rubi_test, If, IntQuadraticQ, IntBinomialQ, RectifyTangent,
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RectifyCotangent, Inequality, Condition, Simp, SimpHelp, SplitProduct,
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SplitSum, SubstFor, SubstForAux, FresnelS, FresnelC, Erfc, Erfi, Gamma,
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FunctionOfTrigOfLinearQ, ElementaryFunctionQ, Complex, UnsameQ,
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_SimpFixFactor, SimpFixFactor, _FixSimplify, FixSimplify,
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_SimplifyAntiderivativeSum, SimplifyAntiderivativeSum,
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_SimplifyAntiderivative, SimplifyAntiderivative, _TrigSimplifyAux,
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TrigSimplifyAux, Cancel, Part, PolyLog, D, Dist, Sum_doit, PolynomialQuotient, Floor,
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PolynomialRemainder, Factor, PolyLog, CosIntegral, SinIntegral, LogIntegral, SinhIntegral,
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CoshIntegral, Rule, Erf, PolyGamma, ExpIntegralEi, ExpIntegralE, LogGamma , UtilityOperator, Factorial,
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Zeta, ProductLog, DerivativeDivides, HypergeometricPFQ, IntHide, OneQ, Null, rubi_exp as exp, rubi_log as log, Discriminant,
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Negative, Quotient
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)
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from sympy.core.add import Add
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from sympy.core.mod import Mod
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from sympy.core.mul import Mul
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from sympy.core import EulerGamma
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from sympy.core.numbers import (Float, I, Integer)
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from sympy.core.power import Pow
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from sympy.core.singleton import S
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from sympy.functions.elementary.complexes import (Abs, sign)
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.integrals.integrals import Integral
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from sympy.logic.boolalg import (And, Or)
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from sympy.simplify.simplify import simplify
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from sympy.integrals.rubi.symbol import WC
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from sympy.core.symbol import symbols, Symbol
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from sympy.functions import (sin, cos, tan, cot, csc, sec, sqrt, erf)
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from sympy.functions.elementary.hyperbolic import (acosh, asinh, atanh, acoth, acsch, asech, cosh, sinh, tanh, coth, sech, csch)
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from sympy.functions.elementary.trigonometric import (atan, acsc, asin, acot, acos, asec, atan2)
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from sympy.core.numbers import pi as Pi
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A_, B_, C_, F_, G_, H_, a_, b_, c_, d_, e_, f_, g_, h_, i_, j_, k_, l_, m_, n_, p_, q_, r_, t_, u_, v_, s_, w_, x_, y_, z_ = [WC(i) for i in 'ABCFGHabcdefghijklmnpqrtuvswxyz']
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a1_, a2_, b1_, b2_, c1_, c2_, d1_, d2_, n1_, n2_, e1_, e2_, f1_, f2_, g1_, g2_, n1_, n2_, n3_, Pq_, Pm_, Px_, Qm_, Qr_, Qx_, jn_, mn_, non2_, RFx_, RGx_ = [WC(i) for i in ['a1', 'a2', 'b1', 'b2', 'c1', 'c2', 'd1', 'd2', 'n1', 'n2', 'e1', 'e2', 'f1', 'f2', 'g1', 'g2', 'n1', 'n2', 'n3', 'Pq', 'Pm', 'Px', 'Qm', 'Qr', 'Qx', 'jn', 'mn', 'non2', 'RFx', 'RGx']]
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i, ii, Pqq, Q, R, r, C, k, u = symbols('i ii Pqq Q R r C k u')
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_UseGamma = False
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ShowSteps = False
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StepCounter = None
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def hyperbolic():
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from sympy.integrals.rubi.constraints import cons33, cons170, cons8, cons29, cons50, cons127, cons96, cons1118, cons178, cons1490, cons19, cons89, cons167, cons3, cons95, cons168, cons87, cons1491, cons247, cons249, cons91, cons1444, cons150, cons1861, cons2, cons1492, cons1441, cons810, cons1493, cons1494, cons1456, cons1442, cons64, cons1269, cons1495, cons812, cons813, cons4, cons1362, cons130, cons40, cons139, cons746, cons65, cons1496, cons198, cons1497, cons5, cons55, cons13, cons598, cons1498, cons20, cons1499, cons378, cons148, cons491, cons1500, cons70, cons71, cons825, cons826, cons1501, cons1503, cons1257, cons1504, cons58, cons152, cons1505, cons1506, cons685, cons369, cons1507, cons358, cons68, cons856, cons25, cons1508, cons56, cons14, cons820, cons1133, cons1134, cons1135, cons1509, cons821, cons530, cons1267, cons1512, cons21, cons1573, cons1574, cons1575, cons1576, cons1577, cons1578, cons1579, cons1580, cons1581, cons1045, cons1582, cons1646, cons1738, cons1647, cons586, cons466, cons1685, cons1410, cons1686, cons1687, cons1862, cons1863, cons1690, cons814, cons815, cons557, cons1864, cons1865, cons27, cons1693, cons1866, cons1101, cons1867, cons1868, cons1397, cons1869, cons1695, cons1870, cons965, cons1871, cons1872, cons210, cons1702, cons1013, cons1553, cons1703, cons1704, cons211, cons226, cons1701, cons1873, cons1705, cons1706, cons1874, cons1708, cons1709, cons1875, cons1876, cons1877, cons1878, cons1879, cons1880, cons1881, cons1882, cons1883, cons1884, cons1885, cons1886, cons1887, cons1888, cons1722, cons1889, cons1890, cons1891, cons1725, cons1892, cons165, cons340, cons164, cons629, cons73, cons1727, cons1728, cons1729, cons90, cons1730, cons1458, cons465, cons1731, cons1480, cons1732, cons1893, cons36, cons37, cons1476, cons1483, cons1735
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pattern5646 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons170)
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rule5646 = ReplacementRule(pattern5646, replacement5646)
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pattern5647 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons170)
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rule5647 = ReplacementRule(pattern5647, replacement5647)
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pattern5648 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons96)
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rule5648 = ReplacementRule(pattern5648, replacement5648)
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pattern5649 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons96)
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rule5649 = ReplacementRule(pattern5649, replacement5649)
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pattern5650 = Pattern(Integral(sinh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons1118)
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rule5650 = ReplacementRule(pattern5650, replacement5650)
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pattern5651 = Pattern(Integral(cosh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons1118)
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rule5651 = ReplacementRule(pattern5651, replacement5651)
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pattern5652 = Pattern(Integral(sinh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons178)
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rule5652 = ReplacementRule(pattern5652, replacement5652)
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pattern5653 = Pattern(Integral(cosh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons178)
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rule5653 = ReplacementRule(pattern5653, replacement5653)
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pattern5654 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons19, cons1490)
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rule5654 = ReplacementRule(pattern5654, replacement5654)
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pattern5655 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons19, cons1490)
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rule5655 = ReplacementRule(pattern5655, replacement5655)
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pattern5656 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons167)
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rule5656 = ReplacementRule(pattern5656, replacement5656)
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pattern5657 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons167)
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rule5657 = ReplacementRule(pattern5657, replacement5657)
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pattern5658 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons168)
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rule5658 = ReplacementRule(pattern5658, replacement5658)
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pattern5659 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons168)
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rule5659 = ReplacementRule(pattern5659, replacement5659)
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pattern5660 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons1491)
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rule5660 = ReplacementRule(pattern5660, replacement5660)
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pattern5661 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons1491)
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rule5661 = ReplacementRule(pattern5661, replacement5661)
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pattern5662 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons33, cons247)
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rule5662 = ReplacementRule(pattern5662, replacement5662)
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pattern5663 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons33, cons247)
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rule5663 = ReplacementRule(pattern5663, replacement5663)
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pattern5664 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons249)
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rule5664 = ReplacementRule(pattern5664, replacement5664)
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pattern5665 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons249)
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rule5665 = ReplacementRule(pattern5665, replacement5665)
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pattern5666 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons91, cons1444)
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rule5666 = ReplacementRule(pattern5666, replacement5666)
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pattern5667 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons91, cons1444)
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rule5667 = ReplacementRule(pattern5667, replacement5667)
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pattern5668 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons3, cons8, cons29, cons50, cons127, cons95, cons91, cons1444, cons168)
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rule5668 = ReplacementRule(pattern5668, replacement5668)
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pattern5669 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons3, cons8, cons29, cons50, cons127, cons95, cons91, cons1444, cons168)
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rule5669 = ReplacementRule(pattern5669, replacement5669)
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pattern5670 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons150, cons1861)
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rule5670 = ReplacementRule(pattern5670, replacement5670)
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pattern5671 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons150, cons1492)
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rule5671 = ReplacementRule(pattern5671, replacement5671)
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pattern5672 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1441, cons87)
|
|
rule5672 = ReplacementRule(pattern5672, replacement5672)
|
|
|
|
pattern5673 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1441, cons810, cons1493)
|
|
rule5673 = ReplacementRule(pattern5673, replacement5673)
|
|
|
|
pattern5674 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1494, cons87)
|
|
rule5674 = ReplacementRule(pattern5674, replacement5674)
|
|
|
|
pattern5675 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1456, cons87)
|
|
rule5675 = ReplacementRule(pattern5675, replacement5675)
|
|
|
|
pattern5676 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1494, cons810, cons1493)
|
|
rule5676 = ReplacementRule(pattern5676, replacement5676)
|
|
|
|
pattern5677 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1456, cons810, cons1493)
|
|
rule5677 = ReplacementRule(pattern5677, replacement5677)
|
|
|
|
pattern5678 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons64)
|
|
rule5678 = ReplacementRule(pattern5678, replacement5678)
|
|
|
|
pattern5679 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64)
|
|
rule5679 = ReplacementRule(pattern5679, replacement5679)
|
|
|
|
pattern5680 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons64)
|
|
rule5680 = ReplacementRule(pattern5680, replacement5680)
|
|
|
|
pattern5681 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64)
|
|
rule5681 = ReplacementRule(pattern5681, replacement5681)
|
|
|
|
pattern5682 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons1495, cons64)
|
|
rule5682 = ReplacementRule(pattern5682, replacement5682)
|
|
|
|
pattern5683 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons1495, cons64)
|
|
rule5683 = ReplacementRule(pattern5683, replacement5683)
|
|
|
|
pattern5684 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813)
|
|
rule5684 = ReplacementRule(pattern5684, replacement5684)
|
|
|
|
pattern5685 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813)
|
|
rule5685 = ReplacementRule(pattern5685, replacement5685)
|
|
|
|
pattern5686 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362)
|
|
rule5686 = ReplacementRule(pattern5686, replacement5686)
|
|
|
|
pattern5687 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362)
|
|
rule5687 = ReplacementRule(pattern5687, replacement5687)
|
|
|
|
pattern5688 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons130)
|
|
rule5688 = ReplacementRule(pattern5688, replacement5688)
|
|
|
|
pattern5689 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons130)
|
|
rule5689 = ReplacementRule(pattern5689, replacement5689)
|
|
|
|
pattern5690 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons139, cons746)
|
|
rule5690 = ReplacementRule(pattern5690, replacement5690)
|
|
|
|
pattern5691 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons139, cons746)
|
|
rule5691 = ReplacementRule(pattern5691, replacement5691)
|
|
|
|
pattern5692 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons150, cons1496)
|
|
rule5692 = ReplacementRule(pattern5692, replacement5692)
|
|
|
|
pattern5693 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons150, cons1496)
|
|
rule5693 = ReplacementRule(pattern5693, replacement5693)
|
|
|
|
pattern5694 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons198)
|
|
rule5694 = ReplacementRule(pattern5694, replacement5694)
|
|
|
|
pattern5695 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons198)
|
|
rule5695 = ReplacementRule(pattern5695, replacement5695)
|
|
|
|
pattern5696 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5696 = ReplacementRule(pattern5696, replacement5696)
|
|
|
|
pattern5697 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5697 = ReplacementRule(pattern5697, replacement5697)
|
|
|
|
pattern5698 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130)
|
|
rule5698 = ReplacementRule(pattern5698, replacement5698)
|
|
|
|
pattern5699 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130)
|
|
rule5699 = ReplacementRule(pattern5699, replacement5699)
|
|
|
|
pattern5700 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons55, cons13, cons139, cons598)
|
|
rule5700 = ReplacementRule(pattern5700, replacement5700)
|
|
|
|
pattern5701 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons55, cons13, cons139, cons598)
|
|
rule5701 = ReplacementRule(pattern5701, replacement5701)
|
|
|
|
pattern5702 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons33, cons139, cons1498)
|
|
rule5702 = ReplacementRule(pattern5702, replacement5702)
|
|
|
|
pattern5703 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons33, cons139, cons1498)
|
|
rule5703 = ReplacementRule(pattern5703, replacement5703)
|
|
|
|
pattern5704 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons20, cons150, cons1496)
|
|
rule5704 = ReplacementRule(pattern5704, replacement5704)
|
|
|
|
pattern5705 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons20, cons150, cons1496)
|
|
rule5705 = ReplacementRule(pattern5705, replacement5705)
|
|
|
|
pattern5706 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons65, cons198)
|
|
rule5706 = ReplacementRule(pattern5706, replacement5706)
|
|
|
|
pattern5707 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons65, cons198)
|
|
rule5707 = ReplacementRule(pattern5707, replacement5707)
|
|
|
|
pattern5708 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5708 = ReplacementRule(pattern5708, replacement5708)
|
|
|
|
pattern5709 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5709 = ReplacementRule(pattern5709, replacement5709)
|
|
|
|
pattern5710 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons87, cons167)
|
|
rule5710 = ReplacementRule(pattern5710, replacement5710)
|
|
|
|
pattern5711 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons87, cons167)
|
|
rule5711 = ReplacementRule(pattern5711, replacement5711)
|
|
|
|
pattern5712 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons378, cons167, cons148)
|
|
rule5712 = ReplacementRule(pattern5712, replacement5712)
|
|
|
|
pattern5713 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons378, cons167, cons148)
|
|
rule5713 = ReplacementRule(pattern5713, replacement5713)
|
|
|
|
pattern5714 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198)
|
|
rule5714 = ReplacementRule(pattern5714, replacement5714)
|
|
|
|
pattern5715 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198)
|
|
rule5715 = ReplacementRule(pattern5715, replacement5715)
|
|
|
|
pattern5716 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons491)
|
|
rule5716 = ReplacementRule(pattern5716, With5716)
|
|
|
|
pattern5717 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons491)
|
|
rule5717 = ReplacementRule(pattern5717, With5717)
|
|
|
|
pattern5718 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons4, cons1500)
|
|
rule5718 = ReplacementRule(pattern5718, replacement5718)
|
|
|
|
pattern5719 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons4, cons1500)
|
|
rule5719 = ReplacementRule(pattern5719, replacement5719)
|
|
|
|
pattern5720 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons130)
|
|
rule5720 = ReplacementRule(pattern5720, replacement5720)
|
|
|
|
pattern5721 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons130)
|
|
rule5721 = ReplacementRule(pattern5721, replacement5721)
|
|
|
|
pattern5722 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons40, cons70, cons71)
|
|
rule5722 = ReplacementRule(pattern5722, replacement5722)
|
|
|
|
pattern5723 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons40, cons70, cons71)
|
|
rule5723 = ReplacementRule(pattern5723, replacement5723)
|
|
|
|
pattern5724 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70)
|
|
rule5724 = ReplacementRule(pattern5724, replacement5724)
|
|
|
|
pattern5725 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70)
|
|
rule5725 = ReplacementRule(pattern5725, replacement5725)
|
|
|
|
pattern5726 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5726 = ReplacementRule(pattern5726, replacement5726)
|
|
|
|
pattern5727 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5727 = ReplacementRule(pattern5727, replacement5727)
|
|
|
|
pattern5728 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)))/x_, x_), cons29, cons4, cons1501)
|
|
rule5728 = ReplacementRule(pattern5728, replacement5728)
|
|
|
|
pattern5729 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)))/x_, x_), cons29, cons4, cons1501)
|
|
rule5729 = ReplacementRule(pattern5729, replacement5729)
|
|
|
|
pattern5730 = Pattern(Integral(sinh(c_ + x_**n_*WC('d', S(1)))/x_, x_), cons8, cons29, cons4, cons1500)
|
|
rule5730 = ReplacementRule(pattern5730, replacement5730)
|
|
|
|
pattern5731 = Pattern(Integral(cosh(c_ + x_**n_*WC('d', S(1)))/x_, x_), cons8, cons29, cons4, cons1500)
|
|
rule5731 = ReplacementRule(pattern5731, replacement5731)
|
|
|
|
pattern5732 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, CustomConstraint(With5732))
|
|
rule5732 = ReplacementRule(pattern5732, replacement5732)
|
|
|
|
pattern5733 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, CustomConstraint(With5733))
|
|
rule5733 = ReplacementRule(pattern5733, replacement5733)
|
|
|
|
pattern5734 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, CustomConstraint(With5734))
|
|
rule5734 = ReplacementRule(pattern5734, replacement5734)
|
|
|
|
pattern5735 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, CustomConstraint(With5735))
|
|
rule5735 = ReplacementRule(pattern5735, replacement5735)
|
|
|
|
pattern5736 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons1503)
|
|
rule5736 = ReplacementRule(pattern5736, replacement5736)
|
|
|
|
pattern5737 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons1503)
|
|
rule5737 = ReplacementRule(pattern5737, replacement5737)
|
|
|
|
pattern5738 = Pattern(Integral((x_*WC('e', S(1)))**m_*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons96)
|
|
rule5738 = ReplacementRule(pattern5738, replacement5738)
|
|
|
|
pattern5739 = Pattern(Integral((x_*WC('e', S(1)))**m_*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons96)
|
|
rule5739 = ReplacementRule(pattern5739, replacement5739)
|
|
|
|
pattern5740 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons150)
|
|
rule5740 = ReplacementRule(pattern5740, replacement5740)
|
|
|
|
pattern5741 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons150)
|
|
rule5741 = ReplacementRule(pattern5741, replacement5741)
|
|
|
|
pattern5742 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons378, cons1257, cons148, cons1504)
|
|
rule5742 = ReplacementRule(pattern5742, replacement5742)
|
|
|
|
pattern5743 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons378, cons1257, cons148, cons1504)
|
|
rule5743 = ReplacementRule(pattern5743, replacement5743)
|
|
|
|
pattern5744 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons148)
|
|
rule5744 = ReplacementRule(pattern5744, replacement5744)
|
|
|
|
pattern5745 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons148)
|
|
rule5745 = ReplacementRule(pattern5745, replacement5745)
|
|
|
|
pattern5746 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1505)
|
|
rule5746 = ReplacementRule(pattern5746, replacement5746)
|
|
|
|
pattern5747 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1505)
|
|
rule5747 = ReplacementRule(pattern5747, replacement5747)
|
|
|
|
pattern5748 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1506, cons685)
|
|
rule5748 = ReplacementRule(pattern5748, replacement5748)
|
|
|
|
pattern5749 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1506, cons685)
|
|
rule5749 = ReplacementRule(pattern5749, replacement5749)
|
|
|
|
pattern5750 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons150, cons369)
|
|
rule5750 = ReplacementRule(pattern5750, With5750)
|
|
|
|
pattern5751 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons150, cons369)
|
|
rule5751 = ReplacementRule(pattern5751, With5751)
|
|
|
|
pattern5752 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons150, cons148)
|
|
rule5752 = ReplacementRule(pattern5752, replacement5752)
|
|
|
|
pattern5753 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons150, cons148)
|
|
rule5753 = ReplacementRule(pattern5753, replacement5753)
|
|
|
|
pattern5754 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons139, cons1507)
|
|
rule5754 = ReplacementRule(pattern5754, replacement5754)
|
|
|
|
pattern5755 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons139, cons1507)
|
|
rule5755 = ReplacementRule(pattern5755, replacement5755)
|
|
|
|
pattern5756 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons139, cons1507, cons1505)
|
|
rule5756 = ReplacementRule(pattern5756, replacement5756)
|
|
|
|
pattern5757 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons139, cons1507, cons1505)
|
|
rule5757 = ReplacementRule(pattern5757, replacement5757)
|
|
|
|
pattern5758 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198, cons20)
|
|
rule5758 = ReplacementRule(pattern5758, replacement5758)
|
|
|
|
pattern5759 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198, cons20)
|
|
rule5759 = ReplacementRule(pattern5759, replacement5759)
|
|
|
|
pattern5760 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons198, cons369)
|
|
rule5760 = ReplacementRule(pattern5760, With5760)
|
|
|
|
pattern5761 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons198, cons369)
|
|
rule5761 = ReplacementRule(pattern5761, With5761)
|
|
|
|
pattern5762 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons198, cons358)
|
|
rule5762 = ReplacementRule(pattern5762, replacement5762)
|
|
|
|
pattern5763 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons198, cons358)
|
|
rule5763 = ReplacementRule(pattern5763, replacement5763)
|
|
|
|
pattern5764 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons40, cons491)
|
|
rule5764 = ReplacementRule(pattern5764, With5764)
|
|
|
|
pattern5765 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons40, cons491)
|
|
rule5765 = ReplacementRule(pattern5765, With5765)
|
|
|
|
pattern5766 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons491)
|
|
rule5766 = ReplacementRule(pattern5766, replacement5766)
|
|
|
|
pattern5767 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons491)
|
|
rule5767 = ReplacementRule(pattern5767, replacement5767)
|
|
|
|
pattern5768 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, cons68, cons856, cons25)
|
|
rule5768 = ReplacementRule(pattern5768, replacement5768)
|
|
|
|
pattern5769 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, cons68, cons856, cons25)
|
|
rule5769 = ReplacementRule(pattern5769, replacement5769)
|
|
|
|
pattern5770 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons68, cons856, cons25)
|
|
rule5770 = ReplacementRule(pattern5770, replacement5770)
|
|
|
|
pattern5771 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons68, cons856, cons25)
|
|
rule5771 = ReplacementRule(pattern5771, replacement5771)
|
|
|
|
pattern5772 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons4, cons1508)
|
|
rule5772 = ReplacementRule(pattern5772, replacement5772)
|
|
|
|
pattern5773 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons4, cons1508)
|
|
rule5773 = ReplacementRule(pattern5773, replacement5773)
|
|
|
|
pattern5774 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130)
|
|
rule5774 = ReplacementRule(pattern5774, replacement5774)
|
|
|
|
pattern5775 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130)
|
|
rule5775 = ReplacementRule(pattern5775, replacement5775)
|
|
|
|
pattern5776 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71, cons20)
|
|
rule5776 = ReplacementRule(pattern5776, replacement5776)
|
|
|
|
pattern5777 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71, cons20)
|
|
rule5777 = ReplacementRule(pattern5777, replacement5777)
|
|
|
|
pattern5778 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons70)
|
|
rule5778 = ReplacementRule(pattern5778, replacement5778)
|
|
|
|
pattern5779 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons70)
|
|
rule5779 = ReplacementRule(pattern5779, replacement5779)
|
|
|
|
pattern5780 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5780 = ReplacementRule(pattern5780, replacement5780)
|
|
|
|
pattern5781 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5781 = ReplacementRule(pattern5781, replacement5781)
|
|
|
|
pattern5782 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons19, cons4, cons5, cons55, cons56)
|
|
rule5782 = ReplacementRule(pattern5782, replacement5782)
|
|
|
|
pattern5783 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons19, cons4, cons5, cons55, cons56)
|
|
rule5783 = ReplacementRule(pattern5783, replacement5783)
|
|
|
|
pattern5784 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons95, cons1503, cons56)
|
|
rule5784 = ReplacementRule(pattern5784, replacement5784)
|
|
|
|
pattern5785 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons5, cons95, cons1503, cons56)
|
|
rule5785 = ReplacementRule(pattern5785, replacement5785)
|
|
|
|
pattern5786 = Pattern(Integral(sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons14)
|
|
rule5786 = ReplacementRule(pattern5786, replacement5786)
|
|
|
|
pattern5787 = Pattern(Integral(cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons14)
|
|
rule5787 = ReplacementRule(pattern5787, replacement5787)
|
|
|
|
pattern5788 = Pattern(Integral(sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons87, cons167)
|
|
rule5788 = ReplacementRule(pattern5788, replacement5788)
|
|
|
|
pattern5789 = Pattern(Integral(cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons87, cons167)
|
|
rule5789 = ReplacementRule(pattern5789, replacement5789)
|
|
|
|
pattern5790 = Pattern(Integral(sinh(v_)**WC('n', S(1)), x_), cons150, cons820, cons1133)
|
|
rule5790 = ReplacementRule(pattern5790, replacement5790)
|
|
|
|
pattern5791 = Pattern(Integral(cosh(v_)**WC('n', S(1)), x_), cons150, cons820, cons1133)
|
|
rule5791 = ReplacementRule(pattern5791, replacement5791)
|
|
|
|
pattern5792 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1134)
|
|
rule5792 = ReplacementRule(pattern5792, replacement5792)
|
|
|
|
pattern5793 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1134)
|
|
rule5793 = ReplacementRule(pattern5793, replacement5793)
|
|
|
|
pattern5794 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1135)
|
|
rule5794 = ReplacementRule(pattern5794, replacement5794)
|
|
|
|
pattern5795 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1135)
|
|
rule5795 = ReplacementRule(pattern5795, replacement5795)
|
|
|
|
pattern5796 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1134)
|
|
rule5796 = ReplacementRule(pattern5796, replacement5796)
|
|
|
|
pattern5797 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1134)
|
|
rule5797 = ReplacementRule(pattern5797, replacement5797)
|
|
|
|
pattern5798 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1135)
|
|
rule5798 = ReplacementRule(pattern5798, replacement5798)
|
|
|
|
pattern5799 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1135)
|
|
rule5799 = ReplacementRule(pattern5799, replacement5799)
|
|
|
|
pattern5800 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1134)
|
|
rule5800 = ReplacementRule(pattern5800, replacement5800)
|
|
|
|
pattern5801 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1134)
|
|
rule5801 = ReplacementRule(pattern5801, replacement5801)
|
|
|
|
pattern5802 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1135)
|
|
rule5802 = ReplacementRule(pattern5802, replacement5802)
|
|
|
|
pattern5803 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1135)
|
|
rule5803 = ReplacementRule(pattern5803, replacement5803)
|
|
|
|
pattern5804 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons1509)
|
|
rule5804 = ReplacementRule(pattern5804, replacement5804)
|
|
|
|
pattern5805 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons1509)
|
|
rule5805 = ReplacementRule(pattern5805, replacement5805)
|
|
|
|
pattern5806 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons87, cons167)
|
|
rule5806 = ReplacementRule(pattern5806, replacement5806)
|
|
|
|
pattern5807 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons87, cons167)
|
|
rule5807 = ReplacementRule(pattern5807, replacement5807)
|
|
|
|
pattern5808 = Pattern(Integral(u_**WC('m', S(1))*sinh(v_)**WC('n', S(1)), x_), cons19, cons150, cons70, cons820, cons821)
|
|
rule5808 = ReplacementRule(pattern5808, replacement5808)
|
|
|
|
pattern5809 = Pattern(Integral(u_**WC('m', S(1))*cosh(v_)**WC('n', S(1)), x_), cons19, cons150, cons70, cons820, cons821)
|
|
rule5809 = ReplacementRule(pattern5809, replacement5809)
|
|
|
|
pattern5810 = Pattern(Integral((x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons2, cons3, cons50, cons127, cons64)
|
|
rule5810 = ReplacementRule(pattern5810, replacement5810)
|
|
|
|
pattern5811 = Pattern(Integral((x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons2, cons3, cons50, cons127, cons64)
|
|
rule5811 = ReplacementRule(pattern5811, replacement5811)
|
|
|
|
pattern5812 = Pattern(Integral((WC('c', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons167, cons170)
|
|
rule5812 = ReplacementRule(pattern5812, replacement5812)
|
|
|
|
pattern5813 = Pattern(Integral((WC('c', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons167, cons170)
|
|
rule5813 = ReplacementRule(pattern5813, replacement5813)
|
|
|
|
pattern5814 = Pattern(Integral((WC('c', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons91, cons170)
|
|
rule5814 = ReplacementRule(pattern5814, replacement5814)
|
|
|
|
pattern5815 = Pattern(Integral((WC('c', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons91, cons170)
|
|
rule5815 = ReplacementRule(pattern5815, replacement5815)
|
|
|
|
pattern5816 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530)
|
|
rule5816 = ReplacementRule(pattern5816, replacement5816)
|
|
|
|
pattern5817 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530)
|
|
rule5817 = ReplacementRule(pattern5817, replacement5817)
|
|
|
|
pattern5818 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons170)
|
|
rule5818 = ReplacementRule(pattern5818, replacement5818)
|
|
|
|
pattern5819 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons170)
|
|
rule5819 = ReplacementRule(pattern5819, replacement5819)
|
|
|
|
pattern5820 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267)
|
|
rule5820 = ReplacementRule(pattern5820, replacement5820)
|
|
|
|
pattern5821 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267)
|
|
rule5821 = ReplacementRule(pattern5821, replacement5821)
|
|
|
|
pattern5822 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons96, cons1512)
|
|
rule5822 = ReplacementRule(pattern5822, replacement5822)
|
|
|
|
pattern5823 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons96, cons1512)
|
|
rule5823 = ReplacementRule(pattern5823, replacement5823)
|
|
|
|
pattern5824 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267)
|
|
rule5824 = ReplacementRule(pattern5824, replacement5824)
|
|
|
|
pattern5825 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267)
|
|
rule5825 = ReplacementRule(pattern5825, replacement5825)
|
|
|
|
pattern5826 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons21)
|
|
rule5826 = ReplacementRule(pattern5826, replacement5826)
|
|
|
|
pattern5827 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons21)
|
|
rule5827 = ReplacementRule(pattern5827, replacement5827)
|
|
|
|
pattern5828 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1573)
|
|
rule5828 = ReplacementRule(pattern5828, replacement5828)
|
|
|
|
pattern5829 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1573)
|
|
rule5829 = ReplacementRule(pattern5829, replacement5829)
|
|
|
|
pattern5830 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons198)
|
|
rule5830 = ReplacementRule(pattern5830, replacement5830)
|
|
|
|
pattern5831 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons198)
|
|
rule5831 = ReplacementRule(pattern5831, replacement5831)
|
|
|
|
pattern5832 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1574, cons33, cons170)
|
|
rule5832 = ReplacementRule(pattern5832, With5832)
|
|
|
|
pattern5833 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1574, cons33, cons170)
|
|
rule5833 = ReplacementRule(pattern5833, With5833)
|
|
|
|
pattern5834 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64)
|
|
rule5834 = ReplacementRule(pattern5834, replacement5834)
|
|
|
|
pattern5835 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64)
|
|
rule5835 = ReplacementRule(pattern5835, replacement5835)
|
|
|
|
pattern5836 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269)
|
|
rule5836 = ReplacementRule(pattern5836, replacement5836)
|
|
|
|
pattern5837 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269)
|
|
rule5837 = ReplacementRule(pattern5837, replacement5837)
|
|
|
|
pattern5838 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons198, cons64)
|
|
rule5838 = ReplacementRule(pattern5838, replacement5838)
|
|
|
|
pattern5839 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons198, cons64)
|
|
rule5839 = ReplacementRule(pattern5839, replacement5839)
|
|
|
|
pattern5840 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813)
|
|
rule5840 = ReplacementRule(pattern5840, replacement5840)
|
|
|
|
pattern5841 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813)
|
|
rule5841 = ReplacementRule(pattern5841, replacement5841)
|
|
|
|
pattern5842 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362)
|
|
rule5842 = ReplacementRule(pattern5842, replacement5842)
|
|
|
|
pattern5843 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362)
|
|
rule5843 = ReplacementRule(pattern5843, replacement5843)
|
|
|
|
pattern5844 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40)
|
|
rule5844 = ReplacementRule(pattern5844, replacement5844)
|
|
|
|
pattern5845 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40)
|
|
rule5845 = ReplacementRule(pattern5845, replacement5845)
|
|
|
|
pattern5846 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5846 = ReplacementRule(pattern5846, replacement5846)
|
|
|
|
pattern5847 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5847 = ReplacementRule(pattern5847, replacement5847)
|
|
|
|
pattern5848 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71)
|
|
rule5848 = ReplacementRule(pattern5848, replacement5848)
|
|
|
|
pattern5849 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71)
|
|
rule5849 = ReplacementRule(pattern5849, replacement5849)
|
|
|
|
pattern5850 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5850 = ReplacementRule(pattern5850, replacement5850)
|
|
|
|
pattern5851 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5851 = ReplacementRule(pattern5851, replacement5851)
|
|
|
|
pattern5852 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40)
|
|
rule5852 = ReplacementRule(pattern5852, replacement5852)
|
|
|
|
pattern5853 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40)
|
|
rule5853 = ReplacementRule(pattern5853, replacement5853)
|
|
|
|
pattern5854 = Pattern(Integral(x_**WC('m', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons8, cons29, cons19, cons4, cons1577)
|
|
rule5854 = ReplacementRule(pattern5854, replacement5854)
|
|
|
|
pattern5855 = Pattern(Integral(x_**WC('m', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons8, cons29, cons19, cons4, cons1577)
|
|
rule5855 = ReplacementRule(pattern5855, replacement5855)
|
|
|
|
pattern5856 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578)
|
|
rule5856 = ReplacementRule(pattern5856, replacement5856)
|
|
|
|
pattern5857 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578)
|
|
rule5857 = ReplacementRule(pattern5857, replacement5857)
|
|
|
|
pattern5858 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5858 = ReplacementRule(pattern5858, replacement5858)
|
|
|
|
pattern5859 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5859 = ReplacementRule(pattern5859, replacement5859)
|
|
|
|
pattern5860 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5860 = ReplacementRule(pattern5860, replacement5860)
|
|
|
|
pattern5861 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5861 = ReplacementRule(pattern5861, replacement5861)
|
|
|
|
pattern5862 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*tanh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1580)
|
|
rule5862 = ReplacementRule(pattern5862, replacement5862)
|
|
|
|
pattern5863 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*(S(1)/tanh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('q', S(1)), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1580)
|
|
rule5863 = ReplacementRule(pattern5863, replacement5863)
|
|
|
|
pattern5864 = Pattern(Integral(tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons4, cons1581)
|
|
rule5864 = ReplacementRule(pattern5864, replacement5864)
|
|
|
|
pattern5865 = Pattern(Integral((S(1)/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons4, cons1581)
|
|
rule5865 = ReplacementRule(pattern5865, replacement5865)
|
|
|
|
pattern5866 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1045)
|
|
rule5866 = ReplacementRule(pattern5866, replacement5866)
|
|
|
|
pattern5867 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1045)
|
|
rule5867 = ReplacementRule(pattern5867, replacement5867)
|
|
|
|
pattern5868 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons1582)
|
|
rule5868 = ReplacementRule(pattern5868, replacement5868)
|
|
|
|
pattern5869 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*(S(1)/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons1582)
|
|
rule5869 = ReplacementRule(pattern5869, replacement5869)
|
|
|
|
pattern5870 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons64)
|
|
rule5870 = ReplacementRule(pattern5870, replacement5870)
|
|
|
|
pattern5871 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons64)
|
|
rule5871 = ReplacementRule(pattern5871, replacement5871)
|
|
|
|
pattern5872 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons33, cons170)
|
|
rule5872 = ReplacementRule(pattern5872, replacement5872)
|
|
|
|
pattern5873 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons33, cons170)
|
|
rule5873 = ReplacementRule(pattern5873, replacement5873)
|
|
|
|
pattern5874 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons167, cons1646)
|
|
rule5874 = ReplacementRule(pattern5874, replacement5874)
|
|
|
|
pattern5875 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons167, cons1646)
|
|
rule5875 = ReplacementRule(pattern5875, replacement5875)
|
|
|
|
pattern5876 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons167, cons1646, cons168)
|
|
rule5876 = ReplacementRule(pattern5876, replacement5876)
|
|
|
|
pattern5877 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons167, cons1646, cons168)
|
|
rule5877 = ReplacementRule(pattern5877, replacement5877)
|
|
|
|
pattern5878 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons91)
|
|
rule5878 = ReplacementRule(pattern5878, replacement5878)
|
|
|
|
pattern5879 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons91)
|
|
rule5879 = ReplacementRule(pattern5879, replacement5879)
|
|
|
|
pattern5880 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons91, cons168)
|
|
rule5880 = ReplacementRule(pattern5880, replacement5880)
|
|
|
|
pattern5881 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons91, cons168)
|
|
rule5881 = ReplacementRule(pattern5881, replacement5881)
|
|
|
|
pattern5882 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons25)
|
|
rule5882 = ReplacementRule(pattern5882, replacement5882)
|
|
|
|
pattern5883 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons25)
|
|
rule5883 = ReplacementRule(pattern5883, replacement5883)
|
|
|
|
pattern5884 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530)
|
|
rule5884 = ReplacementRule(pattern5884, replacement5884)
|
|
|
|
pattern5885 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530)
|
|
rule5885 = ReplacementRule(pattern5885, replacement5885)
|
|
|
|
pattern5886 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons198, cons64)
|
|
rule5886 = ReplacementRule(pattern5886, replacement5886)
|
|
|
|
pattern5887 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons198, cons64)
|
|
rule5887 = ReplacementRule(pattern5887, replacement5887)
|
|
|
|
pattern5888 = Pattern(Integral(u_**WC('m', S(1))*(S(1)/cosh(v_))**WC('n', S(1)), x_), cons19, cons4, cons812, cons813)
|
|
rule5888 = ReplacementRule(pattern5888, replacement5888)
|
|
|
|
pattern5889 = Pattern(Integral(u_**WC('m', S(1))*(S(1)/sinh(v_))**WC('n', S(1)), x_), cons19, cons4, cons812, cons813)
|
|
rule5889 = ReplacementRule(pattern5889, replacement5889)
|
|
|
|
pattern5890 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1738)
|
|
rule5890 = ReplacementRule(pattern5890, replacement5890)
|
|
|
|
pattern5891 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1738)
|
|
rule5891 = ReplacementRule(pattern5891, replacement5891)
|
|
|
|
pattern5892 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40)
|
|
rule5892 = ReplacementRule(pattern5892, replacement5892)
|
|
|
|
pattern5893 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40)
|
|
rule5893 = ReplacementRule(pattern5893, replacement5893)
|
|
|
|
pattern5894 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5894 = ReplacementRule(pattern5894, replacement5894)
|
|
|
|
pattern5895 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497)
|
|
rule5895 = ReplacementRule(pattern5895, replacement5895)
|
|
|
|
pattern5896 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71)
|
|
rule5896 = ReplacementRule(pattern5896, replacement5896)
|
|
|
|
pattern5897 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71)
|
|
rule5897 = ReplacementRule(pattern5897, replacement5897)
|
|
|
|
pattern5898 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5898 = ReplacementRule(pattern5898, replacement5898)
|
|
|
|
pattern5899 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826)
|
|
rule5899 = ReplacementRule(pattern5899, replacement5899)
|
|
|
|
pattern5900 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40)
|
|
rule5900 = ReplacementRule(pattern5900, replacement5900)
|
|
|
|
pattern5901 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40)
|
|
rule5901 = ReplacementRule(pattern5901, replacement5901)
|
|
|
|
pattern5902 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578)
|
|
rule5902 = ReplacementRule(pattern5902, replacement5902)
|
|
|
|
pattern5903 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578)
|
|
rule5903 = ReplacementRule(pattern5903, replacement5903)
|
|
|
|
pattern5904 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5904 = ReplacementRule(pattern5904, replacement5904)
|
|
|
|
pattern5905 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499)
|
|
rule5905 = ReplacementRule(pattern5905, replacement5905)
|
|
|
|
pattern5906 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5906 = ReplacementRule(pattern5906, replacement5906)
|
|
|
|
pattern5907 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826)
|
|
rule5907 = ReplacementRule(pattern5907, replacement5907)
|
|
|
|
pattern5908 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**p_*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1647)
|
|
rule5908 = ReplacementRule(pattern5908, replacement5908)
|
|
|
|
pattern5909 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**p_*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1647)
|
|
rule5909 = ReplacementRule(pattern5909, replacement5909)
|
|
|
|
pattern5910 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586)
|
|
rule5910 = ReplacementRule(pattern5910, replacement5910)
|
|
|
|
pattern5911 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586)
|
|
rule5911 = ReplacementRule(pattern5911, replacement5911)
|
|
|
|
pattern5912 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466)
|
|
rule5912 = ReplacementRule(pattern5912, replacement5912)
|
|
|
|
pattern5913 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466)
|
|
rule5913 = ReplacementRule(pattern5913, replacement5913)
|
|
|
|
pattern5914 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466)
|
|
rule5914 = ReplacementRule(pattern5914, replacement5914)
|
|
|
|
pattern5915 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons1685, cons33, cons170)
|
|
rule5915 = ReplacementRule(pattern5915, replacement5915)
|
|
|
|
pattern5916 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons1685, cons33, cons170)
|
|
rule5916 = ReplacementRule(pattern5916, replacement5916)
|
|
|
|
pattern5917 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586)
|
|
rule5917 = ReplacementRule(pattern5917, replacement5917)
|
|
|
|
pattern5918 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586)
|
|
rule5918 = ReplacementRule(pattern5918, replacement5918)
|
|
|
|
pattern5919 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**p_/cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons1410)
|
|
rule5919 = ReplacementRule(pattern5919, replacement5919)
|
|
|
|
pattern5920 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1410)
|
|
rule5920 = ReplacementRule(pattern5920, replacement5920)
|
|
|
|
pattern5921 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**p_/sinh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons1410)
|
|
rule5921 = ReplacementRule(pattern5921, replacement5921)
|
|
|
|
pattern5922 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1410)
|
|
rule5922 = ReplacementRule(pattern5922, replacement5922)
|
|
|
|
pattern5923 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons64, cons1686)
|
|
rule5923 = ReplacementRule(pattern5923, With5923)
|
|
|
|
pattern5924 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons64, cons1686)
|
|
rule5924 = ReplacementRule(pattern5924, With5924)
|
|
|
|
pattern5925 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons33, cons87)
|
|
rule5925 = ReplacementRule(pattern5925, replacement5925)
|
|
|
|
pattern5926 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons378, cons33, cons170, cons1687)
|
|
rule5926 = ReplacementRule(pattern5926, With5926)
|
|
|
|
pattern5927 = Pattern(Integral(F_**v_*G_**w_*u_**WC('m', S(1)), x_), cons19, cons4, cons5, cons1862, cons1863, cons1690, cons814, cons815)
|
|
rule5927 = ReplacementRule(pattern5927, replacement5927)
|
|
|
|
pattern5928 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5928 = ReplacementRule(pattern5928, replacement5928)
|
|
|
|
pattern5929 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5929 = ReplacementRule(pattern5929, replacement5929)
|
|
|
|
pattern5930 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/cosh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5930 = ReplacementRule(pattern5930, replacement5930)
|
|
|
|
pattern5931 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/sinh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5931 = ReplacementRule(pattern5931, replacement5931)
|
|
|
|
pattern5932 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*tanh(x_*WC('d', S(1)) + WC('c', S(0)))/cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5932 = ReplacementRule(pattern5932, replacement5932)
|
|
|
|
pattern5933 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/(sinh(x_*WC('d', S(1)) + WC('c', S(0)))*tanh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586)
|
|
rule5933 = ReplacementRule(pattern5933, replacement5933)
|
|
|
|
pattern5934 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons557, cons20)
|
|
rule5934 = ReplacementRule(pattern5934, replacement5934)
|
|
|
|
pattern5935 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons557, cons20)
|
|
rule5935 = ReplacementRule(pattern5935, replacement5935)
|
|
|
|
pattern5936 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons557)
|
|
rule5936 = ReplacementRule(pattern5936, replacement5936)
|
|
|
|
pattern5937 = Pattern(Integral(F_**(x_*WC('b', S(1)) + WC('a', S(0)))*G_**(x_*WC('d', S(1)) + WC('c', S(0)))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1864, cons1865, cons557, cons27, cons1693)
|
|
rule5937 = ReplacementRule(pattern5937, replacement5937)
|
|
|
|
pattern5938 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1866)
|
|
rule5938 = ReplacementRule(pattern5938, replacement5938)
|
|
|
|
pattern5939 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1866)
|
|
rule5939 = ReplacementRule(pattern5939, replacement5939)
|
|
|
|
pattern5940 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1867, cons89, cons167)
|
|
rule5940 = ReplacementRule(pattern5940, replacement5940)
|
|
|
|
pattern5941 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1867, cons89, cons167)
|
|
rule5941 = ReplacementRule(pattern5941, replacement5941)
|
|
|
|
pattern5942 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1868, cons586, cons1397)
|
|
rule5942 = ReplacementRule(pattern5942, replacement5942)
|
|
|
|
pattern5943 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1868, cons586, cons1397)
|
|
rule5943 = ReplacementRule(pattern5943, replacement5943)
|
|
|
|
pattern5944 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1869, cons89, cons91, cons1444)
|
|
rule5944 = ReplacementRule(pattern5944, replacement5944)
|
|
|
|
pattern5945 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1869, cons89, cons91, cons1444)
|
|
rule5945 = ReplacementRule(pattern5945, replacement5945)
|
|
|
|
pattern5946 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons25)
|
|
rule5946 = ReplacementRule(pattern5946, replacement5946)
|
|
|
|
pattern5947 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons25)
|
|
rule5947 = ReplacementRule(pattern5947, replacement5947)
|
|
|
|
pattern5948 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87)
|
|
rule5948 = ReplacementRule(pattern5948, replacement5948)
|
|
|
|
pattern5949 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/tanh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87)
|
|
rule5949 = ReplacementRule(pattern5949, replacement5949)
|
|
|
|
pattern5950 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1695, cons89, cons91)
|
|
rule5950 = ReplacementRule(pattern5950, replacement5950)
|
|
|
|
pattern5951 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1695, cons89, cons91)
|
|
rule5951 = ReplacementRule(pattern5951, replacement5951)
|
|
|
|
pattern5952 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1870, cons1504, cons965)
|
|
rule5952 = ReplacementRule(pattern5952, replacement5952)
|
|
|
|
pattern5953 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1870, cons1504, cons965)
|
|
rule5953 = ReplacementRule(pattern5953, replacement5953)
|
|
|
|
pattern5954 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1871, cons89, cons167, cons1646)
|
|
rule5954 = ReplacementRule(pattern5954, replacement5954)
|
|
|
|
pattern5955 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1871, cons89, cons167, cons1646)
|
|
rule5955 = ReplacementRule(pattern5955, replacement5955)
|
|
|
|
pattern5956 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87)
|
|
rule5956 = ReplacementRule(pattern5956, replacement5956)
|
|
|
|
pattern5957 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87)
|
|
rule5957 = ReplacementRule(pattern5957, replacement5957)
|
|
|
|
pattern5958 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons25)
|
|
rule5958 = ReplacementRule(pattern5958, replacement5958)
|
|
|
|
pattern5959 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons25)
|
|
rule5959 = ReplacementRule(pattern5959, replacement5959)
|
|
|
|
pattern5960 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1872, cons198)
|
|
rule5960 = ReplacementRule(pattern5960, replacement5960)
|
|
|
|
pattern5961 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1702, cons198)
|
|
rule5961 = ReplacementRule(pattern5961, replacement5961)
|
|
|
|
pattern5962 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1013, cons198)
|
|
rule5962 = ReplacementRule(pattern5962, replacement5962)
|
|
|
|
pattern5963 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1872, cons152, cons1553)
|
|
rule5963 = ReplacementRule(pattern5963, replacement5963)
|
|
|
|
pattern5964 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1702, cons152, cons1553)
|
|
rule5964 = ReplacementRule(pattern5964, replacement5964)
|
|
|
|
pattern5965 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1013, cons152, cons1553)
|
|
rule5965 = ReplacementRule(pattern5965, replacement5965)
|
|
|
|
pattern5966 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(h_ + WC('i', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))/(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons211, cons226, cons1872, cons1703, cons1704)
|
|
rule5966 = ReplacementRule(pattern5966, replacement5966)
|
|
|
|
pattern5967 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(h_ + WC('i', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))/(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons211, cons226, cons1701, cons1873, cons1705)
|
|
rule5967 = ReplacementRule(pattern5967, replacement5967)
|
|
|
|
pattern5968 = Pattern(Integral(F_**(u_*WC('c', S(1)))*G_**v_, x_), cons1101, cons8, cons4, cons1863, cons812, cons813)
|
|
rule5968 = ReplacementRule(pattern5968, replacement5968)
|
|
|
|
pattern5969 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('m', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons33, cons170, cons150)
|
|
rule5969 = ReplacementRule(pattern5969, With5969)
|
|
|
|
pattern5970 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('m', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons33, cons170, cons150)
|
|
rule5970 = ReplacementRule(pattern5970, With5970)
|
|
|
|
pattern5971 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_*WC('g', S(1)) + WC('f', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons530)
|
|
rule5971 = ReplacementRule(pattern5971, replacement5971)
|
|
|
|
pattern5972 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('p', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_*WC('g', S(1)) + WC('f', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1706)
|
|
rule5972 = ReplacementRule(pattern5972, replacement5972)
|
|
|
|
pattern5973 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*G_**(x_*WC('e', S(1)) + WC('d', S(0)))*H_**(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons530, cons1863, cons1874)
|
|
rule5973 = ReplacementRule(pattern5973, replacement5973)
|
|
|
|
pattern5974 = Pattern(Integral(F_**u_*sinh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons150)
|
|
rule5974 = ReplacementRule(pattern5974, replacement5974)
|
|
|
|
pattern5975 = Pattern(Integral(F_**u_*cosh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons150)
|
|
rule5975 = ReplacementRule(pattern5975, replacement5975)
|
|
|
|
pattern5976 = Pattern(Integral(F_**u_*sinh(v_)**WC('m', S(1))*cosh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons530)
|
|
rule5976 = ReplacementRule(pattern5976, replacement5976)
|
|
|
|
pattern5977 = Pattern(Integral(sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons8, cons1875)
|
|
rule5977 = ReplacementRule(pattern5977, replacement5977)
|
|
|
|
pattern5978 = Pattern(Integral(cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons8, cons1875)
|
|
rule5978 = ReplacementRule(pattern5978, replacement5978)
|
|
|
|
pattern5979 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1876, cons56)
|
|
rule5979 = ReplacementRule(pattern5979, replacement5979)
|
|
|
|
pattern5980 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1876, cons56)
|
|
rule5980 = ReplacementRule(pattern5980, replacement5980)
|
|
|
|
pattern5981 = Pattern(Integral(sqrt(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))), x_), cons2, cons3, cons8, cons4, cons1877)
|
|
rule5981 = ReplacementRule(pattern5981, replacement5981)
|
|
|
|
pattern5982 = Pattern(Integral(sqrt(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))), x_), cons2, cons3, cons8, cons4, cons1877)
|
|
rule5982 = ReplacementRule(pattern5982, replacement5982)
|
|
|
|
pattern5983 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons130, cons1878)
|
|
rule5983 = ReplacementRule(pattern5983, replacement5983)
|
|
|
|
pattern5984 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons130, cons1878)
|
|
rule5984 = ReplacementRule(pattern5984, replacement5984)
|
|
|
|
pattern5985 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1879)
|
|
rule5985 = ReplacementRule(pattern5985, replacement5985)
|
|
|
|
pattern5986 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1879)
|
|
rule5986 = ReplacementRule(pattern5986, replacement5986)
|
|
|
|
pattern5987 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1880)
|
|
rule5987 = ReplacementRule(pattern5987, replacement5987)
|
|
|
|
pattern5988 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1880)
|
|
rule5988 = ReplacementRule(pattern5988, replacement5988)
|
|
|
|
pattern5989 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1507, cons1881)
|
|
rule5989 = ReplacementRule(pattern5989, replacement5989)
|
|
|
|
pattern5990 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1507, cons1881)
|
|
rule5990 = ReplacementRule(pattern5990, replacement5990)
|
|
|
|
pattern5991 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1880)
|
|
rule5991 = ReplacementRule(pattern5991, replacement5991)
|
|
|
|
pattern5992 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1880)
|
|
rule5992 = ReplacementRule(pattern5992, replacement5992)
|
|
|
|
pattern5993 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1882, cons56, cons68)
|
|
rule5993 = ReplacementRule(pattern5993, replacement5993)
|
|
|
|
pattern5994 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1882, cons56, cons68)
|
|
rule5994 = ReplacementRule(pattern5994, replacement5994)
|
|
|
|
pattern5995 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons130, cons1883)
|
|
rule5995 = ReplacementRule(pattern5995, replacement5995)
|
|
|
|
pattern5996 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons130, cons1883)
|
|
rule5996 = ReplacementRule(pattern5996, replacement5996)
|
|
|
|
pattern5997 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1884, cons68)
|
|
rule5997 = ReplacementRule(pattern5997, replacement5997)
|
|
|
|
pattern5998 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1884, cons68)
|
|
rule5998 = ReplacementRule(pattern5998, replacement5998)
|
|
|
|
pattern5999 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1885, cons13, cons148, cons68)
|
|
rule5999 = ReplacementRule(pattern5999, replacement5999)
|
|
|
|
pattern6000 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1885, cons13, cons148, cons68)
|
|
rule6000 = ReplacementRule(pattern6000, replacement6000)
|
|
|
|
pattern6001 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1886, cons13, cons139, cons1507, cons68)
|
|
rule6001 = ReplacementRule(pattern6001, replacement6001)
|
|
|
|
pattern6002 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1886, cons13, cons139, cons1507, cons68)
|
|
rule6002 = ReplacementRule(pattern6002, replacement6002)
|
|
|
|
pattern6003 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885)
|
|
rule6003 = ReplacementRule(pattern6003, replacement6003)
|
|
|
|
pattern6004 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885)
|
|
rule6004 = ReplacementRule(pattern6004, replacement6004)
|
|
|
|
pattern6005 = Pattern(Integral((S(1)/cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1875)
|
|
rule6005 = ReplacementRule(pattern6005, replacement6005)
|
|
|
|
pattern6006 = Pattern(Integral((S(1)/sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1875)
|
|
rule6006 = ReplacementRule(pattern6006, replacement6006)
|
|
|
|
pattern6007 = Pattern(Integral(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1887)
|
|
rule6007 = ReplacementRule(pattern6007, replacement6007)
|
|
|
|
pattern6008 = Pattern(Integral(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1887)
|
|
rule6008 = ReplacementRule(pattern6008, replacement6008)
|
|
|
|
pattern6009 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1888, cons1647)
|
|
rule6009 = ReplacementRule(pattern6009, replacement6009)
|
|
|
|
pattern6010 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1888, cons1647)
|
|
rule6010 = ReplacementRule(pattern6010, replacement6010)
|
|
|
|
pattern6011 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1722, cons1889)
|
|
rule6011 = ReplacementRule(pattern6011, replacement6011)
|
|
|
|
pattern6012 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1722, cons1889)
|
|
rule6012 = ReplacementRule(pattern6012, replacement6012)
|
|
|
|
pattern6013 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1880)
|
|
rule6013 = ReplacementRule(pattern6013, replacement6013)
|
|
|
|
pattern6014 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1880)
|
|
rule6014 = ReplacementRule(pattern6014, replacement6014)
|
|
|
|
pattern6015 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons5, cons1880)
|
|
rule6015 = ReplacementRule(pattern6015, replacement6015)
|
|
|
|
pattern6016 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons5, cons1880)
|
|
rule6016 = ReplacementRule(pattern6016, replacement6016)
|
|
|
|
pattern6017 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1890)
|
|
rule6017 = ReplacementRule(pattern6017, replacement6017)
|
|
|
|
pattern6018 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1890)
|
|
rule6018 = ReplacementRule(pattern6018, replacement6018)
|
|
|
|
pattern6019 = Pattern(Integral(x_**WC('m', S(1))/cos(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1891)
|
|
rule6019 = ReplacementRule(pattern6019, replacement6019)
|
|
|
|
pattern6020 = Pattern(Integral(x_**WC('m', S(1))/sin(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1891)
|
|
rule6020 = ReplacementRule(pattern6020, replacement6020)
|
|
|
|
pattern6021 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1725, cons68, cons1647)
|
|
rule6021 = ReplacementRule(pattern6021, replacement6021)
|
|
|
|
pattern6022 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1725, cons68, cons1647)
|
|
rule6022 = ReplacementRule(pattern6022, replacement6022)
|
|
|
|
pattern6023 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons148, cons1722, cons1892)
|
|
rule6023 = ReplacementRule(pattern6023, replacement6023)
|
|
|
|
pattern6024 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons148, cons1722, cons1892)
|
|
rule6024 = ReplacementRule(pattern6024, replacement6024)
|
|
|
|
pattern6025 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons139, cons1885)
|
|
rule6025 = ReplacementRule(pattern6025, replacement6025)
|
|
|
|
pattern6026 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons139, cons1885)
|
|
rule6026 = ReplacementRule(pattern6026, replacement6026)
|
|
|
|
pattern6027 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885)
|
|
rule6027 = ReplacementRule(pattern6027, replacement6027)
|
|
|
|
pattern6028 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885)
|
|
rule6028 = ReplacementRule(pattern6028, replacement6028)
|
|
|
|
pattern6029 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons13, cons165)
|
|
rule6029 = ReplacementRule(pattern6029, replacement6029)
|
|
|
|
pattern6030 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons13, cons165)
|
|
rule6030 = ReplacementRule(pattern6030, replacement6030)
|
|
|
|
pattern6031 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**n_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons340, cons165)
|
|
rule6031 = ReplacementRule(pattern6031, replacement6031)
|
|
|
|
pattern6032 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**n_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons340, cons165)
|
|
rule6032 = ReplacementRule(pattern6032, replacement6032)
|
|
|
|
pattern6033 = Pattern(Integral(x_**WC('m', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons19, cons4, cons55, cons13, cons165)
|
|
rule6033 = ReplacementRule(pattern6033, replacement6033)
|
|
|
|
pattern6034 = Pattern(Integral(x_**WC('m', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons19, cons4, cons55, cons13, cons165)
|
|
rule6034 = ReplacementRule(pattern6034, replacement6034)
|
|
|
|
pattern6035 = Pattern(Integral(x_**m_*log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons164, cons165, cons629)
|
|
rule6035 = ReplacementRule(pattern6035, replacement6035)
|
|
|
|
pattern6036 = Pattern(Integral(x_**m_*log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons164, cons165, cons629)
|
|
rule6036 = ReplacementRule(pattern6036, replacement6036)
|
|
|
|
pattern6037 = Pattern(Integral(sinh(WC('a', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons8, cons29, cons150)
|
|
rule6037 = ReplacementRule(pattern6037, replacement6037)
|
|
|
|
pattern6038 = Pattern(Integral(cosh(WC('a', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons8, cons29, cons150)
|
|
rule6038 = ReplacementRule(pattern6038, replacement6038)
|
|
|
|
pattern6039 = Pattern(Integral(sinh((x_*WC('b', S(1)) + WC('a', S(0)))*WC('e', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons150, cons73)
|
|
rule6039 = ReplacementRule(pattern6039, replacement6039)
|
|
|
|
pattern6040 = Pattern(Integral(cosh((x_*WC('b', S(1)) + WC('a', S(0)))*WC('e', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons150, cons73)
|
|
rule6040 = ReplacementRule(pattern6040, replacement6040)
|
|
|
|
pattern6041 = Pattern(Integral(sinh(u_)**WC('n', S(1)), x_), cons150, cons1727)
|
|
rule6041 = ReplacementRule(pattern6041, With6041)
|
|
|
|
pattern6042 = Pattern(Integral(cosh(u_)**WC('n', S(1)), x_), cons150, cons1727)
|
|
rule6042 = ReplacementRule(pattern6042, With6042)
|
|
|
|
pattern6043 = Pattern(Integral(WC('u', S(1))*sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons1690)
|
|
rule6043 = ReplacementRule(pattern6043, replacement6043)
|
|
|
|
pattern6044 = Pattern(Integral(WC('u', S(1))*cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1690)
|
|
rule6044 = ReplacementRule(pattern6044, replacement6044)
|
|
|
|
pattern6045 = Pattern(Integral(sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons557, cons1728)
|
|
rule6045 = ReplacementRule(pattern6045, replacement6045)
|
|
|
|
pattern6046 = Pattern(Integral(cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons557, cons1728)
|
|
rule6046 = ReplacementRule(pattern6046, replacement6046)
|
|
|
|
pattern6047 = Pattern(Integral(x_**WC('m', S(1))*sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons1729, cons1728)
|
|
rule6047 = ReplacementRule(pattern6047, replacement6047)
|
|
|
|
pattern6048 = Pattern(Integral(x_**WC('m', S(1))*cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1729, cons1728)
|
|
rule6048 = ReplacementRule(pattern6048, replacement6048)
|
|
|
|
pattern6049 = Pattern(Integral(WC('u', S(1))*sinh(v_)**WC('p', S(1))*cosh(w_)**WC('p', S(1)), x_), cons1690, cons40)
|
|
rule6049 = ReplacementRule(pattern6049, replacement6049)
|
|
|
|
pattern6050 = Pattern(Integral(sinh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons557, cons1728)
|
|
rule6050 = ReplacementRule(pattern6050, replacement6050)
|
|
|
|
pattern6051 = Pattern(Integral(x_**WC('m', S(1))*sinh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1729, cons1728)
|
|
rule6051 = ReplacementRule(pattern6051, replacement6051)
|
|
|
|
pattern6052 = Pattern(Integral(sinh(v_)*tanh(w_)**WC('n', S(1)), x_), cons89, cons90, cons1730)
|
|
rule6052 = ReplacementRule(pattern6052, replacement6052)
|
|
|
|
pattern6053 = Pattern(Integral((S(1)/tanh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730)
|
|
rule6053 = ReplacementRule(pattern6053, replacement6053)
|
|
|
|
pattern6054 = Pattern(Integral((S(1)/tanh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730)
|
|
rule6054 = ReplacementRule(pattern6054, replacement6054)
|
|
|
|
pattern6055 = Pattern(Integral(cosh(v_)*tanh(w_)**WC('n', S(1)), x_), cons89, cons90, cons1730)
|
|
rule6055 = ReplacementRule(pattern6055, replacement6055)
|
|
|
|
pattern6056 = Pattern(Integral((S(1)/cosh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730)
|
|
rule6056 = ReplacementRule(pattern6056, replacement6056)
|
|
|
|
pattern6057 = Pattern(Integral((S(1)/sinh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730)
|
|
rule6057 = ReplacementRule(pattern6057, replacement6057)
|
|
|
|
pattern6058 = Pattern(Integral((S(1)/sinh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730)
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rule6058 = ReplacementRule(pattern6058, replacement6058)
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|
pattern6059 = Pattern(Integral((S(1)/cosh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730)
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rule6059 = ReplacementRule(pattern6059, replacement6059)
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|
|
|
pattern6060 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362)
|
|
rule6060 = ReplacementRule(pattern6060, replacement6060)
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|
|
|
pattern6061 = Pattern(Integral(x_**WC('m', S(1))*(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2))**n_, x_), cons2, cons3, cons8, cons29, cons1458, cons152, cons170, cons465, cons1731)
|
|
rule6061 = ReplacementRule(pattern6061, replacement6061)
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|
|
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pattern6062 = Pattern(Integral(x_**WC('m', S(1))*(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2))**n_, x_), cons2, cons3, cons8, cons29, cons1480, cons152, cons170, cons465, cons1731)
|
|
rule6062 = ReplacementRule(pattern6062, replacement6062)
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|
|
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pattern6063 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh((c_ + x_*WC('d', S(1)))**n_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons13)
|
|
rule6063 = ReplacementRule(pattern6063, replacement6063)
|
|
|
|
pattern6064 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh((c_ + x_*WC('d', S(1)))**n_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons13)
|
|
rule6064 = ReplacementRule(pattern6064, replacement6064)
|
|
|
|
pattern6065 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/(WC('a', S(0)) + WC('b', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('c', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732)
|
|
rule6065 = ReplacementRule(pattern6065, replacement6065)
|
|
|
|
pattern6066 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((b_ + WC('c', S(1))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons3, cons8, cons29, cons50, cons127, cons210, cons64)
|
|
rule6066 = ReplacementRule(pattern6066, replacement6066)
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|
|
|
pattern6067 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((WC('a', S(1))/cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('b', S(0)) + WC('c', S(1))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732)
|
|
rule6067 = ReplacementRule(pattern6067, replacement6067)
|
|
|
|
pattern6068 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((c_ + WC('b', S(1))/tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons3, cons8, cons29, cons50, cons127, cons210, cons64)
|
|
rule6068 = ReplacementRule(pattern6068, replacement6068)
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|
|
|
pattern6069 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((WC('a', S(1))/sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('b', S(1))/tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('c', S(0)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732)
|
|
rule6069 = ReplacementRule(pattern6069, replacement6069)
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|
|
|
pattern6070 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64)
|
|
rule6070 = ReplacementRule(pattern6070, replacement6070)
|
|
|
|
pattern6071 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64)
|
|
rule6071 = ReplacementRule(pattern6071, replacement6071)
|
|
|
|
pattern6072 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1441)
|
|
rule6072 = ReplacementRule(pattern6072, replacement6072)
|
|
|
|
pattern6073 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1267)
|
|
rule6073 = ReplacementRule(pattern6073, replacement6073)
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|
|
|
pattern6074 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1442)
|
|
rule6074 = ReplacementRule(pattern6074, replacement6074)
|
|
|
|
pattern6075 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1269)
|
|
rule6075 = ReplacementRule(pattern6075, replacement6075)
|
|
|
|
pattern6076 = Pattern(Integral((A_ + WC('B', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))*(x_*WC('f', S(1)) + WC('e', S(0)))/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons36, cons37, cons1893)
|
|
rule6076 = ReplacementRule(pattern6076, replacement6076)
|
|
|
|
pattern6077 = Pattern(Integral((A_ + WC('B', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))*(x_*WC('f', S(1)) + WC('e', S(0)))/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons36, cons37, cons1476)
|
|
rule6077 = ReplacementRule(pattern6077, replacement6077)
|
|
|
|
pattern6078 = Pattern(Integral((a_ + WC('b', S(1))*tanh(v_))**WC('n', S(1))*(S(1)/cosh(v_))**WC('m', S(1)), x_), cons2, cons3, cons152, cons1553, cons1483)
|
|
rule6078 = ReplacementRule(pattern6078, replacement6078)
|
|
|
|
pattern6079 = Pattern(Integral((a_ + WC('b', S(1))/tanh(v_))**WC('n', S(1))*(S(1)/sinh(v_))**WC('m', S(1)), x_), cons2, cons3, cons152, cons1553, cons1483)
|
|
rule6079 = ReplacementRule(pattern6079, replacement6079)
|
|
|
|
pattern6080 = Pattern(Integral(WC('u', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons530)
|
|
rule6080 = ReplacementRule(pattern6080, replacement6080)
|
|
|
|
pattern6081 = Pattern(Integral(WC('u', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons530)
|
|
rule6081 = ReplacementRule(pattern6081, replacement6081)
|
|
|
|
pattern6082 = Pattern(Integral(S(1)/(cosh(c_ + x_*WC('d', S(1)))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73)
|
|
rule6082 = ReplacementRule(pattern6082, replacement6082)
|
|
|
|
pattern6083 = Pattern(Integral(S(1)/(sinh(c_ + x_*WC('d', S(1)))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73)
|
|
rule6083 = ReplacementRule(pattern6083, replacement6083)
|
|
|
|
pattern6084 = Pattern(Integral(tanh(c_ + x_*WC('d', S(1)))*tanh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons1735, cons73)
|
|
rule6084 = ReplacementRule(pattern6084, replacement6084)
|
|
|
|
pattern6085 = Pattern(Integral(S(1)/(tanh(c_ + x_*WC('d', S(1)))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73)
|
|
rule6085 = ReplacementRule(pattern6085, replacement6085)
|
|
|
|
pattern6086 = Pattern(Integral((WC('a', S(1))*cosh(v_) + WC('b', S(1))*sinh(v_))**WC('n', S(1))*WC('u', S(1)), x_), cons2, cons3, cons4, cons1267)
|
|
rule6086 = ReplacementRule(pattern6086, replacement6086)
|
|
return [rule5646, rule5647, rule5648, rule5649, rule5650, rule5651, rule5652, rule5653, rule5654, rule5655, rule5656, rule5657, rule5658, rule5659, rule5660, rule5661, rule5662, rule5663, rule5664, rule5665, rule5666, rule5667, rule5668, rule5669, rule5670, rule5671, rule5672, rule5673, rule5674, rule5675, rule5676, rule5677, rule5678, rule5679, rule5680, rule5681, rule5682, rule5683, rule5684, rule5685, rule5686, rule5687, rule5688, rule5689, rule5690, rule5691, rule5692, rule5693, rule5694, rule5695, rule5696, rule5697, rule5698, rule5699, rule5700, rule5701, rule5702, rule5703, rule5704, rule5705, rule5706, rule5707, rule5708, rule5709, rule5710, rule5711, rule5712, rule5713, rule5714, rule5715, rule5716, rule5717, rule5718, rule5719, rule5720, rule5721, rule5722, rule5723, rule5724, rule5725, rule5726, rule5727, rule5728, rule5729, rule5730, rule5731, rule5732, rule5733, rule5734, rule5735, rule5736, rule5737, rule5738, rule5739, rule5740, rule5741, rule5742, rule5743, rule5744, rule5745, rule5746, rule5747, rule5748, rule5749, rule5750, rule5751, rule5752, rule5753, rule5754, rule5755, rule5756, rule5757, rule5758, rule5759, rule5760, rule5761, rule5762, rule5763, rule5764, rule5765, rule5766, rule5767, rule5768, rule5769, rule5770, rule5771, rule5772, rule5773, rule5774, rule5775, rule5776, rule5777, rule5778, rule5779, rule5780, rule5781, rule5782, rule5783, rule5784, rule5785, rule5786, rule5787, rule5788, rule5789, rule5790, rule5791, rule5792, rule5793, rule5794, rule5795, rule5796, rule5797, rule5798, rule5799, rule5800, rule5801, rule5802, rule5803, rule5804, rule5805, rule5806, rule5807, rule5808, rule5809, rule5810, rule5811, rule5812, rule5813, rule5814, rule5815, rule5816, rule5817, rule5818, rule5819, rule5820, rule5821, rule5822, rule5823, rule5824, rule5825, rule5826, rule5827, rule5828, rule5829, rule5830, rule5831, rule5832, rule5833, rule5834, rule5835, rule5836, rule5837, rule5838, rule5839, rule5840, rule5841, rule5842, rule5843, rule5844, rule5845, rule5846, rule5847, rule5848, rule5849, rule5850, rule5851, rule5852, rule5853, rule5854, rule5855, rule5856, rule5857, rule5858, rule5859, rule5860, rule5861, rule5862, rule5863, rule5864, rule5865, rule5866, rule5867, rule5868, rule5869, rule5870, rule5871, rule5872, rule5873, rule5874, rule5875, rule5876, rule5877, rule5878, rule5879, rule5880, rule5881, rule5882, rule5883, rule5884, rule5885, rule5886, rule5887, rule5888, rule5889, rule5890, rule5891, rule5892, rule5893, rule5894, rule5895, rule5896, rule5897, rule5898, rule5899, rule5900, rule5901, rule5902, rule5903, rule5904, rule5905, rule5906, rule5907, rule5908, rule5909, rule5910, rule5911, rule5912, rule5913, rule5914, rule5915, rule5916, rule5917, rule5918, rule5919, rule5920, rule5921, rule5922, rule5923, rule5924, rule5925, rule5926, rule5927, rule5928, rule5929, rule5930, rule5931, rule5932, rule5933, rule5934, rule5935, rule5936, rule5937, rule5938, rule5939, rule5940, rule5941, rule5942, rule5943, rule5944, rule5945, rule5946, rule5947, rule5948, rule5949, rule5950, rule5951, rule5952, rule5953, rule5954, rule5955, rule5956, rule5957, rule5958, rule5959, rule5960, rule5961, rule5962, rule5963, rule5964, rule5965, rule5966, rule5967, rule5968, rule5969, rule5970, rule5971, rule5972, rule5973, rule5974, rule5975, rule5976, rule5977, rule5978, rule5979, rule5980, rule5981, rule5982, rule5983, rule5984, rule5985, rule5986, rule5987, rule5988, rule5989, rule5990, rule5991, rule5992, rule5993, rule5994, rule5995, rule5996, rule5997, rule5998, rule5999, rule6000, rule6001, rule6002, rule6003, rule6004, rule6005, rule6006, rule6007, rule6008, rule6009, rule6010, rule6011, rule6012, rule6013, rule6014, rule6015, rule6016, rule6017, rule6018, rule6019, rule6020, rule6021, rule6022, rule6023, rule6024, rule6025, rule6026, rule6027, rule6028, rule6029, rule6030, rule6031, rule6032, rule6033, rule6034, rule6035, rule6036, rule6037, rule6038, rule6039, rule6040, rule6041, rule6042, rule6043, rule6044, rule6045, rule6046, rule6047, rule6048, rule6049, rule6050, rule6051, rule6052, rule6053, rule6054, rule6055, rule6056, rule6057, rule6058, rule6059, rule6060, rule6061, rule6062, rule6063, rule6064, rule6065, rule6066, rule6067, rule6068, rule6069, rule6070, rule6071, rule6072, rule6073, rule6074, rule6075, rule6076, rule6077, rule6078, rule6079, rule6080, rule6081, rule6082, rule6083, rule6084, rule6085, rule6086, ]
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def replacement5646(c, d, e, f, m, x):
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|
return -Dist(d*m/f, Int((c + d*x)**(m + S(-1))*cosh(e + f*x), x), x) + Simp((c + d*x)**m*cosh(e + f*x)/f, x)
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def replacement5647(c, d, e, f, m, x):
|
|
return -Dist(d*m/f, Int((c + d*x)**(m + S(-1))*sinh(e + f*x), x), x) + Simp((c + d*x)**m*sinh(e + f*x)/f, x)
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|
def replacement5648(c, d, e, f, m, x):
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|
return -Dist(f/(d*(m + S(1))), Int((c + d*x)**(m + S(1))*cosh(e + f*x), x), x) + Simp((c + d*x)**(m + S(1))*sinh(e + f*x)/(d*(m + S(1))), x)
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def replacement5649(c, d, e, f, m, x):
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return -Dist(f/(d*(m + S(1))), Int((c + d*x)**(m + S(1))*sinh(e + f*x), x), x) + Simp((c + d*x)**(m + S(1))*cosh(e + f*x)/(d*(m + S(1))), x)
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def replacement5650(c, d, e, f, x):
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|
return Simp(SinhIntegral(e + f*x)/d, x)
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def replacement5651(c, d, e, f, x):
|
|
return Simp(CoshIntegral(e + f*x)/d, x)
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def replacement5652(c, d, e, f, x):
|
|
return Dist(sinh((-c*f + d*e)/d), Int(cosh(c*f/d + f*x)/(c + d*x), x), x) + Dist(cosh((-c*f + d*e)/d), Int(sinh(c*f/d + f*x)/(c + d*x), x), x)
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def replacement5653(c, d, e, f, x):
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return Dist(sinh((-c*f + d*e)/d), Int(sinh(c*f/d + f*x)/(c + d*x), x), x) + Dist(cosh((-c*f + d*e)/d), Int(cosh(c*f/d + f*x)/(c + d*x), x), x)
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def replacement5654(c, d, e, f, m, x):
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|
return -Dist(S(1)/2, Int((c + d*x)**m*exp(-e - f*x), x), x) + Dist(S(1)/2, Int((c + d*x)**m*exp(e + f*x), x), x)
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def replacement5655(c, d, e, f, m, x):
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return Dist(S(1)/2, Int((c + d*x)**m*exp(-e - f*x), x), x) + Dist(S(1)/2, Int((c + d*x)**m*exp(e + f*x), x), x)
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def replacement5656(b, c, d, e, f, n, x):
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return -Dist(b**S(2)*(n + S(-1))/n, Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x), x), x) - Simp(d*(b*sinh(e + f*x))**n/(f**S(2)*n**S(2)), x) + Simp(b*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)*cosh(e + f*x)/(f*n), x)
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def replacement5657(b, c, d, e, f, n, x):
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return Dist(b**S(2)*(n + S(-1))/n, Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x), x), x) - Simp(d*(b*cosh(e + f*x))**n/(f**S(2)*n**S(2)), x) + Simp(b*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)*sinh(e + f*x)/(f*n), x)
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def replacement5658(b, c, d, e, f, m, n, x):
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return -Dist(b**S(2)*(n + S(-1))/n, Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(f**S(2)*n**S(2)), Int((b*sinh(e + f*x))**n*(c + d*x)**(m + S(-2)), x), x) + Simp(b*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)**m*cosh(e + f*x)/(f*n), x) - Simp(d*m*(b*sinh(e + f*x))**n*(c + d*x)**(m + S(-1))/(f**S(2)*n**S(2)), x)
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def replacement5659(b, c, d, e, f, m, n, x):
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return Dist(b**S(2)*(n + S(-1))/n, Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(f**S(2)*n**S(2)), Int((b*cosh(e + f*x))**n*(c + d*x)**(m + S(-2)), x), x) + Simp(b*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)**m*sinh(e + f*x)/(f*n), x) - Simp(d*m*(b*cosh(e + f*x))**n*(c + d*x)**(m + S(-1))/(f**S(2)*n**S(2)), x)
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def replacement5660(c, d, e, f, m, n, x):
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return Int(ExpandTrigReduce((c + d*x)**m, sinh(e + f*x)**n, x), x)
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def replacement5661(c, d, e, f, m, n, x):
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return Int(ExpandTrigReduce((c + d*x)**m, cosh(e + f*x)**n, x), x)
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def replacement5662(c, d, e, f, m, n, x):
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return -Dist(f*n/(d*(m + S(1))), Int(ExpandTrigReduce((c + d*x)**(m + S(1)), sinh(e + f*x)**(n + S(-1))*cosh(e + f*x), x), x), x) + Simp((c + d*x)**(m + S(1))*sinh(e + f*x)**n/(d*(m + S(1))), x)
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def replacement5663(c, d, e, f, m, n, x):
|
|
return -Dist(f*n/(d*(m + S(1))), Int(ExpandTrigReduce((c + d*x)**(m + S(1)), sinh(e + f*x)*cosh(e + f*x)**(n + S(-1)), x), x), x) + Simp((c + d*x)**(m + S(1))*cosh(e + f*x)**n/(d*(m + S(1))), x)
|
|
|
|
|
|
def replacement5664(b, c, d, e, f, m, n, x):
|
|
return Dist(f**S(2)*n**S(2)/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*sinh(e + f*x))**n*(c + d*x)**(m + S(2)), x), x) + Dist(b**S(2)*f**S(2)*n*(n + S(-1))/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x)**(m + S(2)), x), x) + Simp((b*sinh(e + f*x))**n*(c + d*x)**(m + S(1))/(d*(m + S(1))), x) - Simp(b*f*n*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)**(m + S(2))*cosh(e + f*x)/(d**S(2)*(m + S(1))*(m + S(2))), x)
|
|
|
|
|
|
def replacement5665(b, c, d, e, f, m, n, x):
|
|
return Dist(f**S(2)*n**S(2)/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*cosh(e + f*x))**n*(c + d*x)**(m + S(2)), x), x) - Dist(b**S(2)*f**S(2)*n*(n + S(-1))/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x)**(m + S(2)), x), x) + Simp((b*cosh(e + f*x))**n*(c + d*x)**(m + S(1))/(d*(m + S(1))), x) - Simp(b*f*n*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)**(m + S(2))*sinh(e + f*x)/(d**S(2)*(m + S(1))*(m + S(2))), x)
|
|
|
|
|
|
def replacement5666(b, c, d, e, f, n, x):
|
|
return -Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x), x), x) - Simp(d*(b*sinh(e + f*x))**(n + S(2))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) + Simp((b*sinh(e + f*x))**(n + S(1))*(c + d*x)*cosh(e + f*x)/(b*f*(n + S(1))), x)
|
|
|
|
|
|
def replacement5667(b, c, d, e, f, n, x):
|
|
return Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x), x), x) + Simp(d*(b*cosh(e + f*x))**(n + S(2))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) - Simp((b*cosh(e + f*x))**(n + S(1))*(c + d*x)*sinh(e + f*x)/(b*f*(n + S(1))), x)
|
|
|
|
|
|
def replacement5668(b, c, d, e, f, m, n, x):
|
|
return -Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-2)), x), x) + Simp((b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x)/(b*f*(n + S(1))), x) - Simp(d*m*(b*sinh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5669(b, c, d, e, f, m, n, x):
|
|
return Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x)**m, x), x) - Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-2)), x), x) - Simp((b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x)/(b*f*(n + S(1))), x) + Simp(d*m*(b*cosh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5670(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b*sinh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5671(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b*cosh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5672(a, b, c, d, e, f, m, n, x):
|
|
return Dist((S(2)*a)**n, Int((c + d*x)**m*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5673(a, b, c, d, e, f, m, n, x):
|
|
return Dist((S(2)*a)**IntPart(n)*(a + b*sinh(e + f*x))**FracPart(n)*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5674(a, b, c, d, e, f, m, n, x):
|
|
return Dist((S(2)*a)**n, Int((c + d*x)**m*cosh(e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5675(a, b, c, d, e, f, m, n, x):
|
|
return Dist((-S(2)*a)**n, Int((c + d*x)**m*sinh(e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5676(a, b, c, d, e, f, m, n, x):
|
|
return Dist((S(2)*a)**IntPart(n)*(a + b*cosh(e + f*x))**FracPart(n)*cosh(e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*cosh(e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5677(a, b, c, d, e, f, m, n, x):
|
|
return Dist((-S(2)*a)**IntPart(n)*(a + b*cosh(e + f*x))**FracPart(n)*sinh(e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*sinh(e/S(2) + f*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5678(a, b, c, d, e, f, m, x):
|
|
return Dist(S(-2), Int((c + d*x)**m*exp(e + f*x)/(-S(2)*a*exp(e + f*x) - b*exp(S(2)*e + S(2)*f*x) + b), x), x)
|
|
|
|
|
|
def replacement5679(a, b, c, d, e, f, m, x):
|
|
return Dist(S(2), Int((c + d*x)**m*exp(e + f*x)/(S(2)*a*exp(e + f*x) + b*exp(S(2)*e + S(2)*f*x) + b), x), x)
|
|
|
|
|
|
def replacement5680(a, b, c, d, e, f, m, x):
|
|
return Dist(a/(a**S(2) + b**S(2)), Int((c + d*x)**m/(a + b*sinh(e + f*x)), x), x) + Dist(b*d*m/(f*(a**S(2) + b**S(2))), Int((c + d*x)**(m + S(-1))*cosh(e + f*x)/(a + b*sinh(e + f*x)), x), x) - Simp(b*(c + d*x)**m*cosh(e + f*x)/(f*(a + b*sinh(e + f*x))*(a**S(2) + b**S(2))), x)
|
|
|
|
|
|
def replacement5681(a, b, c, d, e, f, m, x):
|
|
return Dist(a/(a**S(2) - b**S(2)), Int((c + d*x)**m/(a + b*cosh(e + f*x)), x), x) + Dist(b*d*m/(f*(a**S(2) - b**S(2))), Int((c + d*x)**(m + S(-1))*sinh(e + f*x)/(a + b*cosh(e + f*x)), x), x) - Simp(b*(c + d*x)**m*sinh(e + f*x)/(f*(a + b*cosh(e + f*x))*(a**S(2) - b**S(2))), x)
|
|
|
|
|
|
def replacement5682(a, b, c, d, e, f, m, n, x):
|
|
return Dist(a/(a**S(2) + b**S(2)), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m, x), x) - Dist(b*(n + S(2))/((a**S(2) + b**S(2))*(n + S(1))), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x), x), x) - Dist(b*d*m/(f*(a**S(2) + b**S(2))*(n + S(1))), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**(m + S(-1))*cosh(e + f*x), x), x) + Simp(b*(a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x)/(f*(a**S(2) + b**S(2))*(n + S(1))), x)
|
|
|
|
|
|
def replacement5683(a, b, c, d, e, f, m, n, x):
|
|
return Dist(a/(a**S(2) - b**S(2)), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m, x), x) - Dist(b*(n + S(2))/((a**S(2) - b**S(2))*(n + S(1))), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x), x), x) - Dist(b*d*m/(f*(a**S(2) - b**S(2))*(n + S(1))), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**(m + S(-1))*sinh(e + f*x), x), x) + Simp(b*(a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x)/(f*(a**S(2) - b**S(2))*(n + S(1))), x)
|
|
|
|
|
|
def replacement5684(a, b, m, n, u, v, x):
|
|
return Int((a + b*sinh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5685(a, b, m, n, u, v, x):
|
|
return Int((a + b*cosh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5686(a, b, c, d, e, f, m, n, x):
|
|
return Int((a + b*sinh(e + f*x))**n*(c + d*x)**m, x)
|
|
|
|
|
|
def replacement5687(a, b, c, d, e, f, m, n, x):
|
|
return Int((a + b*cosh(e + f*x))**n*(c + d*x)**m, x)
|
|
|
|
|
|
def replacement5688(a, b, c, d, n, p, x):
|
|
return Int(ExpandIntegrand(sinh(c + d*x), (a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5689(a, b, c, d, n, p, x):
|
|
return Int(ExpandIntegrand(cosh(c + d*x), (a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5690(a, b, c, d, n, p, x):
|
|
return -Dist(d/(b*n*(p + S(1))), Int(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) - Dist((S(1) - n)/(b*n*(p + S(1))), Int(x**(-n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5691(a, b, c, d, n, p, x):
|
|
return -Dist(d/(b*n*(p + S(1))), Int(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) - Dist((S(1) - n)/(b*n*(p + S(1))), Int(x**(-n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5692(a, b, c, d, n, p, x):
|
|
return Int(ExpandIntegrand(sinh(c + d*x), (a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5693(a, b, c, d, n, p, x):
|
|
return Int(ExpandIntegrand(cosh(c + d*x), (a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5694(a, b, c, d, n, p, x):
|
|
return Int(x**(n*p)*(a*x**(-n) + b)**p*sinh(c + d*x), x)
|
|
|
|
|
|
def replacement5695(a, b, c, d, n, p, x):
|
|
return Int(x**(n*p)*(a*x**(-n) + b)**p*cosh(c + d*x), x)
|
|
|
|
|
|
def replacement5696(a, b, c, d, n, p, x):
|
|
return Int((a + b*x**n)**p*sinh(c + d*x), x)
|
|
|
|
|
|
def replacement5697(a, b, c, d, n, p, x):
|
|
return Int((a + b*x**n)**p*cosh(c + d*x), x)
|
|
|
|
|
|
def replacement5698(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandIntegrand(sinh(c + d*x), (e*x)**m*(a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5699(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandIntegrand(cosh(c + d*x), (e*x)**m*(a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5700(a, b, c, d, e, m, n, p, x):
|
|
return -Dist(d*e**m/(b*n*(p + S(1))), Int((a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(e**m*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5701(a, b, c, d, e, m, n, p, x):
|
|
return -Dist(d*e**m/(b*n*(p + S(1))), Int((a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(e**m*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5702(a, b, c, d, m, n, p, x):
|
|
return -Dist(d/(b*n*(p + S(1))), Int(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) - Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5703(a, b, c, d, m, n, p, x):
|
|
return -Dist(d/(b*n*(p + S(1))), Int(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) - Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5704(a, b, c, d, m, n, p, x):
|
|
return Int(ExpandIntegrand(sinh(c + d*x), x**m*(a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5705(a, b, c, d, m, n, p, x):
|
|
return Int(ExpandIntegrand(cosh(c + d*x), x**m*(a + b*x**n)**p, x), x)
|
|
|
|
|
|
def replacement5706(a, b, c, d, m, n, p, x):
|
|
return Int(x**(m + n*p)*(a*x**(-n) + b)**p*sinh(c + d*x), x)
|
|
|
|
|
|
def replacement5707(a, b, c, d, m, n, p, x):
|
|
return Int(x**(m + n*p)*(a*x**(-n) + b)**p*cosh(c + d*x), x)
|
|
|
|
|
|
def replacement5708(a, b, c, d, e, m, n, p, x):
|
|
return Int((e*x)**m*(a + b*x**n)**p*sinh(c + d*x), x)
|
|
|
|
|
|
def replacement5709(a, b, c, d, e, m, n, p, x):
|
|
return Int((e*x)**m*(a + b*x**n)**p*cosh(c + d*x), x)
|
|
|
|
|
|
def replacement5710(c, d, n, x):
|
|
return -Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5711(c, d, n, x):
|
|
return Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5712(a, b, c, d, n, p, x):
|
|
return Int(ExpandTrigReduce((a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5713(a, b, c, d, n, p, x):
|
|
return Int(ExpandTrigReduce((a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5714(a, b, c, d, n, p, x):
|
|
return -Subst(Int((a + b*sinh(c + d*x**(-n)))**p/x**S(2), x), x, S(1)/x)
|
|
|
|
|
|
def replacement5715(a, b, c, d, n, p, x):
|
|
return -Subst(Int((a + b*cosh(c + d*x**(-n)))**p/x**S(2), x), x, S(1)/x)
|
|
|
|
|
|
def With5716(a, b, c, d, n, p, x):
|
|
k = Denominator(n)
|
|
return Dist(k, Subst(Int(x**(k + S(-1))*(a + b*sinh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x)
|
|
|
|
|
|
def With5717(a, b, c, d, n, p, x):
|
|
k = Denominator(n)
|
|
return Dist(k, Subst(Int(x**(k + S(-1))*(a + b*cosh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x)
|
|
|
|
|
|
def replacement5718(c, d, n, x):
|
|
return -Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5719(c, d, n, x):
|
|
return Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5720(a, b, c, d, n, p, x):
|
|
return Int(ExpandTrigReduce((a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5721(a, b, c, d, n, p, x):
|
|
return Int(ExpandTrigReduce((a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5722(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*sinh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5723(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*cosh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5724(a, b, c, d, n, p, u, x):
|
|
return Int((a + b*sinh(c + d*u**n))**p, x)
|
|
|
|
|
|
def replacement5725(a, b, c, d, n, p, u, x):
|
|
return Int((a + b*cosh(c + d*u**n))**p, x)
|
|
|
|
|
|
def replacement5726(a, b, p, u, x):
|
|
return Int((a + b*sinh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5727(a, b, p, u, x):
|
|
return Int((a + b*cosh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5728(d, n, x):
|
|
return Simp(SinhIntegral(d*x**n)/n, x)
|
|
|
|
|
|
def replacement5729(d, n, x):
|
|
return Simp(CoshIntegral(d*x**n)/n, x)
|
|
|
|
|
|
def replacement5730(c, d, n, x):
|
|
return Dist(sinh(c), Int(cosh(d*x**n)/x, x), x) + Dist(cosh(c), Int(sinh(d*x**n)/x, x), x)
|
|
|
|
|
|
def replacement5731(c, d, n, x):
|
|
return Dist(sinh(c), Int(sinh(d*x**n)/x, x), x) + Dist(cosh(c), Int(cosh(d*x**n)/x, x), x)
|
|
|
|
|
|
def With5732(a, b, c, d, m, n, p, x):
|
|
if isinstance(x, (int, Integer, float, Float)):
|
|
return False
|
|
mn = (m + S(1))/n
|
|
if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))):
|
|
return True
|
|
return False
|
|
|
|
|
|
def replacement5732(a, b, c, d, m, n, p, x):
|
|
|
|
mn = (m + S(1))/n
|
|
return Dist(S(1)/n, Subst(Int(x**(mn + S(-1))*(a + b*sinh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def With5733(a, b, c, d, m, n, p, x):
|
|
if isinstance(x, (int, Integer, float, Float)):
|
|
return False
|
|
mn = (m + S(1))/n
|
|
if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))):
|
|
return True
|
|
return False
|
|
|
|
|
|
def replacement5733(a, b, c, d, m, n, p, x):
|
|
|
|
mn = (m + S(1))/n
|
|
return Dist(S(1)/n, Subst(Int(x**(mn + S(-1))*(a + b*cosh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def With5734(a, b, c, d, e, m, n, p, x):
|
|
if isinstance(x, (int, Integer, float, Float)):
|
|
return False
|
|
mn = (m + S(1))/n
|
|
if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))):
|
|
return True
|
|
return False
|
|
|
|
|
|
def replacement5734(a, b, c, d, e, m, n, p, x):
|
|
|
|
mn = (m + S(1))/n
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def With5735(a, b, c, d, e, m, n, p, x):
|
|
if isinstance(x, (int, Integer, float, Float)):
|
|
return False
|
|
mn = (m + S(1))/n
|
|
if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))):
|
|
return True
|
|
return False
|
|
|
|
|
|
def replacement5735(a, b, c, d, e, m, n, p, x):
|
|
|
|
mn = (m + S(1))/n
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5736(c, d, e, m, n, x):
|
|
return -Dist(e**n*(m - n + S(1))/(d*n), Int((e*x)**(m - n)*cosh(c + d*x**n), x), x) + Simp(e**(n + S(-1))*(e*x)**(m - n + S(1))*cosh(c + d*x**n)/(d*n), x)
|
|
|
|
|
|
def replacement5737(c, d, e, m, n, x):
|
|
return -Dist(e**n*(m - n + S(1))/(d*n), Int((e*x)**(m - n)*sinh(c + d*x**n), x), x) + Simp(e**(n + S(-1))*(e*x)**(m - n + S(1))*sinh(c + d*x**n)/(d*n), x)
|
|
|
|
|
|
def replacement5738(c, d, e, m, n, x):
|
|
return -Dist(d*e**(-n)*n/(m + S(1)), Int((e*x)**(m + n)*cosh(c + d*x**n), x), x) + Simp((e*x)**(m + S(1))*sinh(c + d*x**n)/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5739(c, d, e, m, n, x):
|
|
return -Dist(d*e**(-n)*n/(m + S(1)), Int((e*x)**(m + n)*sinh(c + d*x**n), x), x) + Simp((e*x)**(m + S(1))*cosh(c + d*x**n)/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5740(c, d, e, m, n, x):
|
|
return -Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5741(c, d, e, m, n, x):
|
|
return Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5742(a, b, m, n, p, x):
|
|
return Dist(b*n*p/(n + S(-1)), Int(sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n), x), x) - Simp(x**(S(1) - n)*sinh(a + b*x**n)**p/(n + S(-1)), x)
|
|
|
|
|
|
def replacement5743(a, b, m, n, p, x):
|
|
return Dist(b*n*p/(n + S(-1)), Int(sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1)), x), x) - Simp(x**(S(1) - n)*cosh(a + b*x**n)**p/(n + S(-1)), x)
|
|
|
|
|
|
def replacement5744(a, b, m, n, p, x):
|
|
return -Dist((p + S(-1))/p, Int(x**m*sinh(a + b*x**n)**(p + S(-2)), x), x) - Simp(sinh(a + b*x**n)**p/(b**S(2)*n*p**S(2)), x) + Simp(x**n*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/(b*n*p), x)
|
|
|
|
|
|
def replacement5745(a, b, m, n, p, x):
|
|
return Dist((p + S(-1))/p, Int(x**m*cosh(a + b*x**n)**(p + S(-2)), x), x) - Simp(cosh(a + b*x**n)**p/(b**S(2)*n*p**S(2)), x) + Simp(x**n*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/(b*n*p), x)
|
|
|
|
|
|
def replacement5746(a, b, m, n, p, x):
|
|
return -Dist((p + S(-1))/p, Int(x**m*sinh(a + b*x**n)**(p + S(-2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*p**S(2)), Int(x**(m - S(2)*n)*sinh(a + b*x**n)**p, x), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*sinh(a + b*x**n)**p/(b**S(2)*n**S(2)*p**S(2)), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/(b*n*p), x)
|
|
|
|
|
|
def replacement5747(a, b, m, n, p, x):
|
|
return Dist((p + S(-1))/p, Int(x**m*cosh(a + b*x**n)**(p + S(-2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*p**S(2)), Int(x**(m - S(2)*n)*cosh(a + b*x**n)**p, x), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*cosh(a + b*x**n)**p/(b**S(2)*n**S(2)*p**S(2)), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/(b*n*p), x)
|
|
|
|
|
|
def replacement5748(a, b, m, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p**S(2)/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*sinh(a + b*x**n)**p, x), x) + Dist(b**S(2)*n**S(2)*p*(p + S(-1))/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*sinh(a + b*x**n)**(p + S(-2)), x), x) + Simp(x**(m + S(1))*sinh(a + b*x**n)**p/(m + S(1)), x) - Simp(b*n*p*x**(m + n + S(1))*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/((m + S(1))*(m + n + S(1))), x)
|
|
|
|
|
|
def replacement5749(a, b, m, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p**S(2)/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*cosh(a + b*x**n)**p, x), x) - Dist(b**S(2)*n**S(2)*p*(p + S(-1))/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*cosh(a + b*x**n)**(p + S(-2)), x), x) + Simp(x**(m + S(1))*cosh(a + b*x**n)**p/(m + S(1)), x) - Simp(b*n*p*x**(m + n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/((m + S(1))*(m + n + S(1))), x)
|
|
|
|
|
|
def With5750(a, b, c, d, e, m, n, p, x):
|
|
k = Denominator(m)
|
|
return Dist(k/e, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*e**(-n)*x**(k*n)))**p, x), x, (e*x)**(S(1)/k)), x)
|
|
|
|
|
|
def With5751(a, b, c, d, e, m, n, p, x):
|
|
k = Denominator(m)
|
|
return Dist(k/e, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*e**(-n)*x**(k*n)))**p, x), x, (e*x)**(S(1)/k)), x)
|
|
|
|
|
|
def replacement5752(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandTrigReduce((e*x)**m, (a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5753(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandTrigReduce((e*x)**m, (a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5754(a, b, m, n, p, x):
|
|
return -Dist((p + S(2))/(p + S(1)), Int(x**m*sinh(a + b*x**n)**(p + S(2)), x), x) - Simp(sinh(a + b*x**n)**(p + S(2))/(b**S(2)*n*(p + S(1))*(p + S(2))), x) + Simp(x**n*sinh(a + b*x**n)**(p + S(1))*cosh(a + b*x**n)/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5755(a, b, m, n, p, x):
|
|
return Dist((p + S(2))/(p + S(1)), Int(x**m*cosh(a + b*x**n)**(p + S(2)), x), x) + Simp(cosh(a + b*x**n)**(p + S(2))/(b**S(2)*n*(p + S(1))*(p + S(2))), x) - Simp(x**n*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5756(a, b, m, n, p, x):
|
|
return -Dist((p + S(2))/(p + S(1)), Int(x**m*sinh(a + b*x**n)**(p + S(2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**(m - S(2)*n)*sinh(a + b*x**n)**(p + S(2)), x), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(1))*cosh(a + b*x**n)/(b*n*(p + S(1))), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*sinh(a + b*x**n)**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x)
|
|
|
|
|
|
def replacement5757(a, b, m, n, p, x):
|
|
return Dist((p + S(2))/(p + S(1)), Int(x**m*cosh(a + b*x**n)**(p + S(2)), x), x) - Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**(m - S(2)*n)*cosh(a + b*x**n)**(p + S(2)), x), x) - Simp(x**(m - n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) + Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*cosh(a + b*x**n)**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x)
|
|
|
|
|
|
def replacement5758(a, b, c, d, m, n, p, x):
|
|
return -Subst(Int(x**(-m + S(-2))*(a + b*sinh(c + d*x**(-n)))**p, x), x, S(1)/x)
|
|
|
|
|
|
def replacement5759(a, b, c, d, m, n, p, x):
|
|
return -Subst(Int(x**(-m + S(-2))*(a + b*cosh(c + d*x**(-n)))**p, x), x, S(1)/x)
|
|
|
|
|
|
def With5760(a, b, c, d, e, m, n, p, x):
|
|
k = Denominator(m)
|
|
return -Dist(k/e, Subst(Int(x**(-k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*e**(-n)*x**(-k*n)))**p, x), x, (e*x)**(-S(1)/k)), x)
|
|
|
|
|
|
def With5761(a, b, c, d, e, m, n, p, x):
|
|
k = Denominator(m)
|
|
return -Dist(k/e, Subst(Int(x**(-k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*e**(-n)*x**(-k*n)))**p, x), x, (e*x)**(-S(1)/k)), x)
|
|
|
|
|
|
def replacement5762(a, b, c, d, e, m, n, p, x):
|
|
return -Dist((e*x)**m*(S(1)/x)**m, Subst(Int(x**(-m + S(-2))*(a + b*sinh(c + d*x**(-n)))**p, x), x, S(1)/x), x)
|
|
|
|
|
|
def replacement5763(a, b, c, d, e, m, n, p, x):
|
|
return -Dist((e*x)**m*(S(1)/x)**m, Subst(Int(x**(-m + S(-2))*(a + b*cosh(c + d*x**(-n)))**p, x), x, S(1)/x), x)
|
|
|
|
|
|
def With5764(a, b, c, d, m, n, p, x):
|
|
k = Denominator(n)
|
|
return Dist(k, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x)
|
|
|
|
|
|
def With5765(a, b, c, d, m, n, p, x):
|
|
k = Denominator(n)
|
|
return Dist(k, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x)
|
|
|
|
|
|
def replacement5766(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5767(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5768(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/(m + S(1)), Subst(Int((a + b*sinh(c + d*x**(n/(m + S(1)))))**p, x), x, x**(m + S(1))), x)
|
|
|
|
|
|
def replacement5769(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/(m + S(1)), Subst(Int((a + b*cosh(c + d*x**(n/(m + S(1)))))**p, x), x, x**(m + S(1))), x)
|
|
|
|
|
|
def replacement5770(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5771(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5772(c, d, e, m, n, x):
|
|
return -Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5773(c, d, e, m, n, x):
|
|
return Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x)
|
|
|
|
|
|
def replacement5774(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandTrigReduce((e*x)**m, (a + b*sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5775(a, b, c, d, e, m, n, p, x):
|
|
return Int(ExpandTrigReduce((e*x)**m, (a + b*cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5776(a, b, c, d, m, n, p, u, x):
|
|
return Dist(Coefficient(u, x, S(1))**(-m + S(-1)), Subst(Int((a + b*sinh(c + d*x**n))**p*(x - Coefficient(u, x, S(0)))**m, x), x, u), x)
|
|
|
|
|
|
def replacement5777(a, b, c, d, m, n, p, u, x):
|
|
return Dist(Coefficient(u, x, S(1))**(-m + S(-1)), Subst(Int((a + b*cosh(c + d*x**n))**p*(x - Coefficient(u, x, S(0)))**m, x), x, u), x)
|
|
|
|
|
|
def replacement5778(a, b, c, d, e, m, n, p, u, x):
|
|
return Int((e*x)**m*(a + b*sinh(c + d*u**n))**p, x)
|
|
|
|
|
|
def replacement5779(a, b, c, d, e, m, n, p, u, x):
|
|
return Int((e*x)**m*(a + b*cosh(c + d*u**n))**p, x)
|
|
|
|
|
|
def replacement5780(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b*sinh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5781(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b*cosh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5782(a, b, m, n, p, x):
|
|
return Simp(sinh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5783(a, b, m, n, p, x):
|
|
return Simp(cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5784(a, b, m, n, p, x):
|
|
return -Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*sinh(a + b*x**n)**(p + S(1)), x), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5785(a, b, m, n, p, x):
|
|
return -Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*cosh(a + b*x**n)**(p + S(1)), x), x) + Simp(x**(m - n + S(1))*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x)
|
|
|
|
|
|
def replacement5786(a, b, c, x):
|
|
return -Dist(S(1)/2, Int(exp(-a - b*x - c*x**S(2)), x), x) + Dist(S(1)/2, Int(exp(a + b*x + c*x**S(2)), x), x)
|
|
|
|
|
|
def replacement5787(a, b, c, x):
|
|
return Dist(S(1)/2, Int(exp(-a - b*x - c*x**S(2)), x), x) + Dist(S(1)/2, Int(exp(a + b*x + c*x**S(2)), x), x)
|
|
|
|
|
|
def replacement5788(a, b, c, n, x):
|
|
return Int(ExpandTrigReduce(sinh(a + b*x + c*x**S(2))**n, x), x)
|
|
|
|
|
|
def replacement5789(a, b, c, n, x):
|
|
return Int(ExpandTrigReduce(cosh(a + b*x + c*x**S(2))**n, x), x)
|
|
|
|
|
|
def replacement5790(n, v, x):
|
|
return Int(sinh(ExpandToSum(v, x))**n, x)
|
|
|
|
|
|
def replacement5791(n, v, x):
|
|
return Int(cosh(ExpandToSum(v, x))**n, x)
|
|
|
|
|
|
def replacement5792(a, b, c, d, e, x):
|
|
return Simp(e*cosh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5793(a, b, c, d, e, x):
|
|
return Simp(e*sinh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5794(a, b, c, d, e, x):
|
|
return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int(sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*cosh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5795(a, b, c, d, e, x):
|
|
return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int(cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*sinh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5796(a, b, c, d, e, m, x):
|
|
return -Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5797(a, b, c, d, e, m, x):
|
|
return -Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5798(a, b, c, d, e, m, x):
|
|
return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int((d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2)), x), x) - Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5799(a, b, c, d, e, m, x):
|
|
return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int((d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2)), x), x) - Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5800(a, b, c, d, e, m, x):
|
|
return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2))/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5801(a, b, c, d, e, m, x):
|
|
return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2))/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5802(a, b, c, d, e, m, x):
|
|
return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*cosh(a + b*x + c*x**S(2)), x), x) - Dist((b*e - S(2)*c*d)/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2))/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5803(a, b, c, d, e, m, x):
|
|
return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*sinh(a + b*x + c*x**S(2)), x), x) - Dist((b*e - S(2)*c*d)/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2))/(e*(m + S(1))), x)
|
|
|
|
|
|
def replacement5804(a, b, c, d, e, m, x):
|
|
return Int((d + e*x)**m*sinh(a + b*x + c*x**S(2)), x)
|
|
|
|
|
|
def replacement5805(a, b, c, d, e, m, x):
|
|
return Int((d + e*x)**m*cosh(a + b*x + c*x**S(2)), x)
|
|
|
|
|
|
def replacement5806(a, b, c, d, e, m, n, x):
|
|
return Int(ExpandTrigReduce((d + e*x)**m, sinh(a + b*x + c*x**S(2))**n, x), x)
|
|
|
|
|
|
def replacement5807(a, b, c, d, e, m, n, x):
|
|
return Int(ExpandTrigReduce((d + e*x)**m, cosh(a + b*x + c*x**S(2))**n, x), x)
|
|
|
|
|
|
def replacement5808(m, n, u, v, x):
|
|
return Int(ExpandToSum(u, x)**m*sinh(ExpandToSum(v, x))**n, x)
|
|
|
|
|
|
def replacement5809(m, n, u, v, x):
|
|
return Int(ExpandToSum(u, x)**m*cosh(ExpandToSum(v, x))**n, x)
|
|
|
|
|
|
def replacement5810(a, b, e, f, m, x):
|
|
return Dist(S(2), Int((a + b*x)**m*exp(S(2)*e + S(2)*f*x)/(exp(S(2)*e + S(2)*f*x) + S(1)), x), x) - Simp((a + b*x)**(m + S(1))/(b*(m + S(1))), x)
|
|
|
|
|
|
def replacement5811(a, b, e, f, m, x):
|
|
return -Dist(S(2), Int((a + b*x)**m*exp(S(2)*e + S(2)*f*x)/(S(1) - exp(S(2)*e + S(2)*f*x)), x), x) - Simp((a + b*x)**(m + S(1))/(b*(m + S(1))), x)
|
|
|
|
|
|
def replacement5812(a, b, c, e, f, m, n, x):
|
|
return Dist(c**S(2), Int((c*tanh(e + f*x))**(n + S(-2))*(a + b*x)**m, x), x) + Dist(b*c*m/(f*(n + S(-1))), Int((c*tanh(e + f*x))**(n + S(-1))*(a + b*x)**(m + S(-1)), x), x) - Simp(c*(c*tanh(e + f*x))**(n + S(-1))*(a + b*x)**m/(f*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5813(a, b, c, e, f, m, n, x):
|
|
return Dist(c**S(2), Int((c/tanh(e + f*x))**(n + S(-2))*(a + b*x)**m, x), x) + Dist(b*c*m/(f*(n + S(-1))), Int((c/tanh(e + f*x))**(n + S(-1))*(a + b*x)**(m + S(-1)), x), x) - Simp(c*(c/tanh(e + f*x))**(n + S(-1))*(a + b*x)**m/(f*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5814(a, b, c, e, f, m, n, x):
|
|
return Dist(c**(S(-2)), Int((c*tanh(e + f*x))**(n + S(2))*(a + b*x)**m, x), x) - Dist(b*m/(c*f*(n + S(1))), Int((c*tanh(e + f*x))**(n + S(1))*(a + b*x)**(m + S(-1)), x), x) + Simp((c*tanh(e + f*x))**(n + S(1))*(a + b*x)**m/(c*f*(n + S(1))), x)
|
|
|
|
|
|
def replacement5815(a, b, c, e, f, m, n, x):
|
|
return Dist(c**(S(-2)), Int((c/tanh(e + f*x))**(n + S(2))*(a + b*x)**m, x), x) - Dist(b*m/(c*f*(n + S(1))), Int((c/tanh(e + f*x))**(n + S(1))*(a + b*x)**(m + S(-1)), x), x) + Simp((c/tanh(e + f*x))**(n + S(1))*(a + b*x)**m/(c*f*(n + S(1))), x)
|
|
|
|
|
|
def replacement5816(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b*tanh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5817(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b/tanh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5818(a, b, c, d, e, f, m, x):
|
|
return Dist(a*d*m/(S(2)*b*f), Int((c + d*x)**(m + S(-1))/(a + b*tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) - Simp(a*(c + d*x)**m/(S(2)*b*f*(a + b*tanh(e + f*x))), x)
|
|
|
|
|
|
def replacement5819(a, b, c, d, e, f, m, x):
|
|
return Dist(a*d*m/(S(2)*b*f), Int((c + d*x)**(m + S(-1))/(a + b/tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) - Simp(a*(c + d*x)**m/(S(2)*b*f*(a + b/tanh(e + f*x))), x)
|
|
|
|
|
|
def replacement5820(a, b, c, d, e, f, x):
|
|
return Dist(f/(a*d), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Dist(f/(b*d), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Simp(S(1)/(d*(a + b*tanh(e + f*x))*(c + d*x)), x)
|
|
|
|
|
|
def replacement5821(a, b, c, d, e, f, x):
|
|
return -Dist(f/(a*d), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Dist(f/(b*d), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Simp(S(1)/(d*(a + b/tanh(e + f*x))*(c + d*x)), x)
|
|
|
|
|
|
def replacement5822(a, b, c, d, e, f, m, x):
|
|
return Dist(S(2)*b*f/(a*d*(m + S(1))), Int((c + d*x)**(m + S(1))/(a + b*tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b*tanh(e + f*x))*(m + S(1))), x) - Simp(f*(c + d*x)**(m + S(2))/(b*d**S(2)*(m + S(1))*(m + S(2))), x)
|
|
|
|
|
|
def replacement5823(a, b, c, d, e, f, m, x):
|
|
return Dist(S(2)*b*f/(a*d*(m + S(1))), Int((c + d*x)**(m + S(1))/(a + b/tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b/tanh(e + f*x))*(m + S(1))), x) - Simp(f*(c + d*x)**(m + S(2))/(b*d**S(2)*(m + S(1))*(m + S(2))), x)
|
|
|
|
|
|
def replacement5824(a, b, c, d, e, f, x):
|
|
return Dist(S(1)/(S(2)*a), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Dist(S(1)/(S(2)*b), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Simp(log(c + d*x)/(S(2)*a*d), x)
|
|
|
|
|
|
def replacement5825(a, b, c, d, e, f, x):
|
|
return -Dist(S(1)/(S(2)*a), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Dist(S(1)/(S(2)*b), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Simp(log(c + d*x)/(S(2)*a*d), x)
|
|
|
|
|
|
def replacement5826(a, b, c, d, e, f, m, x):
|
|
return Dist(S(1)/(S(2)*a), Int((c + d*x)**m*exp(-S(2)*a*(e + f*x)/b), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x)
|
|
|
|
|
|
def replacement5827(a, b, c, d, e, f, m, x):
|
|
return -Dist(S(1)/(S(2)*a), Int((c + d*x)**m*exp(-S(2)*a*(e + f*x)/b), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x)
|
|
|
|
|
|
def replacement5828(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (-sinh(S(2)*e + S(2)*f*x)/(S(2)*b) + cosh(S(2)*e + S(2)*f*x)/(S(2)*a) + S(1)/(S(2)*a))**(-n), x), x)
|
|
|
|
|
|
def replacement5829(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (sinh(S(2)*e + S(2)*f*x)/(S(2)*b) - cosh(S(2)*e + S(2)*f*x)/(S(2)*a) + S(1)/(S(2)*a))**(-n), x), x)
|
|
|
|
|
|
def replacement5830(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (S(1)/(S(2)*a) + exp(-S(2)*a*(e + f*x)/b)/(S(2)*a))**(-n), x), x)
|
|
|
|
|
|
def replacement5831(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (S(1)/(S(2)*a) - exp(-S(2)*a*(e + f*x)/b)/(S(2)*a))**(-n), x), x)
|
|
|
|
|
|
def With5832(a, b, c, d, e, f, m, n, x):
|
|
u = IntHide((a + b*tanh(e + f*x))**n, x)
|
|
return -Dist(d*m, Int(Dist((c + d*x)**(m + S(-1)), u, x), x), x) + Dist((c + d*x)**m, u, x)
|
|
|
|
|
|
def With5833(a, b, c, d, e, f, m, n, x):
|
|
u = IntHide((a + b/tanh(e + f*x))**n, x)
|
|
return -Dist(d*m, Int(Dist((c + d*x)**(m + S(-1)), u, x), x), x) + Dist((c + d*x)**m, u, x)
|
|
|
|
|
|
def replacement5834(a, b, c, d, e, f, m, x):
|
|
return -Dist(S(2)*b, Int((c + d*x)**m/(a**S(2) - b**S(2) + (a - b)**S(2)*exp(-S(2)*e - S(2)*f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a - b)*(m + S(1))), x)
|
|
|
|
|
|
def replacement5835(a, b, c, d, e, f, m, x):
|
|
return Dist(S(2)*b, Int((c + d*x)**m/(a**S(2) - b**S(2) - (a + b)**S(2)*exp(S(2)*e + S(2)*f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b)*(m + S(1))), x)
|
|
|
|
|
|
def replacement5836(a, b, c, d, e, f, x):
|
|
return -Dist(S(1)/(f*(a**S(2) - b**S(2))), Int((-S(2)*a*c*f - S(2)*a*d*f*x + b*d)/(a + b*tanh(e + f*x)), x), x) - Simp((c + d*x)**S(2)/(S(2)*d*(a**S(2) - b**S(2))), x) + Simp(b*(c + d*x)/(f*(a + b*tanh(e + f*x))*(a**S(2) - b**S(2))), x)
|
|
|
|
|
|
def replacement5837(a, b, c, d, e, f, x):
|
|
return -Dist(S(1)/(f*(a**S(2) - b**S(2))), Int((-S(2)*a*c*f - S(2)*a*d*f*x + b*d)/(a + b/tanh(e + f*x)), x), x) - Simp((c + d*x)**S(2)/(S(2)*d*(a**S(2) - b**S(2))), x) + Simp(b*(c + d*x)/(f*(a + b/tanh(e + f*x))*(a**S(2) - b**S(2))), x)
|
|
|
|
|
|
def replacement5838(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (-S(2)*b/(a**S(2) - b**S(2) + (a - b)**S(2)*exp(-S(2)*e - S(2)*f*x)) + S(1)/(a - b))**(-n), x), x)
|
|
|
|
|
|
def replacement5839(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (S(2)*b/(a**S(2) - b**S(2) - (a + b)**S(2)*exp(S(2)*e + S(2)*f*x)) + S(1)/(a + b))**(-n), x), x)
|
|
|
|
|
|
def replacement5840(a, b, m, n, u, v, x):
|
|
return Int((a + b*tanh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5841(a, b, m, n, u, v, x):
|
|
return Int((a + b/tanh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5842(a, b, c, d, e, f, m, n, x):
|
|
return Int((a + b*tanh(e + f*x))**n*(c + d*x)**m, x)
|
|
|
|
|
|
def replacement5843(a, b, c, d, e, f, m, n, x):
|
|
return Int((a + b/tanh(e + f*x))**n*(c + d*x)**m, x)
|
|
|
|
|
|
def replacement5844(a, b, c, d, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b*tanh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5845(a, b, c, d, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/tanh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5846(a, b, c, d, n, p, x):
|
|
return Int((a + b*tanh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5847(a, b, c, d, n, p, x):
|
|
return Int((a + b/tanh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5848(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*tanh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5849(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/tanh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5850(a, b, p, u, x):
|
|
return Int((a + b*tanh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5851(a, b, p, u, x):
|
|
return Int((a + b/tanh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5852(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b*tanh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5853(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/tanh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5854(c, d, m, n, x):
|
|
return Dist((m - n + S(1))/(d*n), Int(x**(m - n)*tanh(c + d*x**n), x), x) + Int(x**m, x) - Simp(x**(m - n + S(1))*tanh(c + d*x**n)/(d*n), x)
|
|
|
|
|
|
def replacement5855(c, d, m, n, x):
|
|
return Dist((m - n + S(1))/(d*n), Int(x**(m - n)/tanh(c + d*x**n), x), x) + Int(x**m, x) - Simp(x**(m - n + S(1))/(d*n*tanh(c + d*x**n)), x)
|
|
|
|
|
|
def replacement5856(a, b, c, d, m, n, p, x):
|
|
return Int(x**m*(a + b*tanh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5857(a, b, c, d, m, n, p, x):
|
|
return Int(x**m*(a + b/tanh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5858(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*tanh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5859(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/tanh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5860(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b*tanh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5861(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b/tanh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5862(a, b, m, n, p, q, x):
|
|
return Dist((m - n + S(1))/(b*n*p), Int(x**(m - n)*(S(1)/cosh(a + b*x**n))**p, x), x) - Simp(x**(m - n + S(1))*(S(1)/cosh(a + b*x**n))**p/(b*n*p), x)
|
|
|
|
|
|
def replacement5863(a, b, m, n, p, q, x):
|
|
return Dist((m - n + S(1))/(b*n*p), Int(x**(m - n)*(S(1)/sinh(a + b*x**n))**p, x), x) - Simp(x**(m - n + S(1))*(S(1)/sinh(a + b*x**n))**p/(b*n*p), x)
|
|
|
|
|
|
def replacement5864(a, b, c, n, x):
|
|
return Int(tanh(a + b*x + c*x**S(2))**n, x)
|
|
|
|
|
|
def replacement5865(a, b, c, n, x):
|
|
return Int((S(1)/tanh(a + b*x + c*x**S(2)))**n, x)
|
|
|
|
|
|
def replacement5866(a, b, c, d, e, x):
|
|
return Dist((-b*e + S(2)*c*d)/(S(2)*c), Int(tanh(a + b*x + c*x**S(2)), x), x) + Simp(e*log(cosh(a + b*x + c*x**S(2)))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5867(a, b, c, d, e, x):
|
|
return Dist((-b*e + S(2)*c*d)/(S(2)*c), Int(S(1)/tanh(a + b*x + c*x**S(2)), x), x) + Simp(e*log(sinh(a + b*x + c*x**S(2)))/(S(2)*c), x)
|
|
|
|
|
|
def replacement5868(a, b, c, d, e, m, n, x):
|
|
return Int((d + e*x)**m*tanh(a + b*x + c*x**S(2))**n, x)
|
|
|
|
|
|
def replacement5869(a, b, c, d, e, m, n, x):
|
|
return Int((d + e*x)**m*(S(1)/tanh(a + b*x + c*x**S(2)))**n, x)
|
|
|
|
|
|
def replacement5870(a, b, c, d, m, x):
|
|
return -Dist(I*d*m/b, Int((c + d*x)**(m + S(-1))*log(-I*exp(a + b*x) + S(1)), x), x) + Dist(I*d*m/b, Int((c + d*x)**(m + S(-1))*log(I*exp(a + b*x) + S(1)), x), x) + Simp(S(2)*(c + d*x)**m*ArcTan(exp(a + b*x))/b, x)
|
|
|
|
|
|
def replacement5871(a, b, c, d, m, x):
|
|
return -Dist(d*m/b, Int((c + d*x)**(m + S(-1))*log(S(1) - exp(a + b*x)), x), x) + Dist(d*m/b, Int((c + d*x)**(m + S(-1))*log(exp(a + b*x) + S(1)), x), x) + Simp(-S(2)*(c + d*x)**m*atanh(exp(a + b*x))/b, x)
|
|
|
|
|
|
def replacement5872(a, b, c, d, m, x):
|
|
return -Dist(d*m/b, Int((c + d*x)**(m + S(-1))*tanh(a + b*x), x), x) + Simp((c + d*x)**m*tanh(a + b*x)/b, x)
|
|
|
|
|
|
def replacement5873(a, b, c, d, m, x):
|
|
return Dist(d*m/b, Int((c + d*x)**(m + S(-1))/tanh(a + b*x), x), x) - Simp((c + d*x)**m/(b*tanh(a + b*x)), x)
|
|
|
|
|
|
def replacement5874(a, b, c, d, n, x):
|
|
return Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) + Simp(d*(S(1)/cosh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) + Simp((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(-2))*tanh(a + b*x)/(b*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5875(a, b, c, d, n, x):
|
|
return -Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) - Simp(d*(S(1)/sinh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) - Simp((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(-2))/(b*(n + S(-1))*tanh(a + b*x)), x)
|
|
|
|
|
|
def replacement5876(a, b, c, d, m, n, x):
|
|
return Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) - Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*(n + S(-2))*(n + S(-1))), Int((c + d*x)**(m + S(-2))*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) + Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(-2))*tanh(a + b*x)/(b*(n + S(-1))), x) + Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5877(a, b, c, d, m, n, x):
|
|
return -Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*(n + S(-2))*(n + S(-1))), Int((c + d*x)**(m + S(-2))*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(-2))/(b*(n + S(-1))*tanh(a + b*x)), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5878(a, b, c, d, n, x):
|
|
return Dist((n + S(1))/n, Int((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(2)), x), x) - Simp(d*(S(1)/cosh(a + b*x))**n/(b**S(2)*n**S(2)), x) - Simp((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(1))*sinh(a + b*x)/(b*n), x)
|
|
|
|
|
|
def replacement5879(a, b, c, d, n, x):
|
|
return -Dist((n + S(1))/n, Int((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(2)), x), x) - Simp(d*(S(1)/sinh(a + b*x))**n/(b**S(2)*n**S(2)), x) - Simp((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(1))*cosh(a + b*x)/(b*n), x)
|
|
|
|
|
|
def replacement5880(a, b, c, d, m, n, x):
|
|
return Dist((n + S(1))/n, Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*n**S(2)), Int((c + d*x)**(m + S(-2))*(S(1)/cosh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(1))*sinh(a + b*x)/(b*n), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**n/(b**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5881(a, b, c, d, m, n, x):
|
|
return -Dist((n + S(1))/n, Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*n**S(2)), Int((c + d*x)**(m + S(-2))*(S(1)/sinh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(1))*cosh(a + b*x)/(b*n), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**n/(b**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5882(a, b, c, d, m, n, x):
|
|
return Dist((S(1)/cosh(a + b*x))**n*cosh(a + b*x)**n, Int((c + d*x)**m*cosh(a + b*x)**(-n), x), x)
|
|
|
|
|
|
def replacement5883(a, b, c, d, m, n, x):
|
|
return Dist((S(1)/sinh(a + b*x))**n*sinh(a + b*x)**n, Int((c + d*x)**m*sinh(a + b*x)**(-n), x), x)
|
|
|
|
|
|
def replacement5884(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b/cosh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5885(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a + b/sinh(e + f*x))**n, x), x)
|
|
|
|
|
|
def replacement5886(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a*cosh(e + f*x) + b)**n*cosh(e + f*x)**(-n), x), x)
|
|
|
|
|
|
def replacement5887(a, b, c, d, e, f, m, n, x):
|
|
return Int(ExpandIntegrand((c + d*x)**m, (a*sinh(e + f*x) + b)**n*sinh(e + f*x)**(-n), x), x)
|
|
|
|
|
|
def replacement5888(m, n, u, v, x):
|
|
return Int((S(1)/cosh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5889(m, n, u, v, x):
|
|
return Int((S(1)/sinh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x)
|
|
|
|
|
|
def replacement5890(a, b, c, d, m, n, x):
|
|
return Int((c + d*x)**m*(S(1)/cosh(a + b*x))**n, x)
|
|
|
|
|
|
def replacement5891(a, b, c, d, m, n, x):
|
|
return Int((c + d*x)**m*(S(1)/sinh(a + b*x))**n, x)
|
|
|
|
|
|
def replacement5892(a, b, c, d, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/cosh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5893(a, b, c, d, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/sinh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5894(a, b, c, d, n, p, x):
|
|
return Int((a + b/cosh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5895(a, b, c, d, n, p, x):
|
|
return Int((a + b/sinh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5896(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/cosh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5897(a, b, c, d, n, p, u, x):
|
|
return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/sinh(c + d*x**n))**p, x), x, u), x)
|
|
|
|
|
|
def replacement5898(a, b, p, u, x):
|
|
return Int((a + b/cosh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5899(a, b, p, u, x):
|
|
return Int((a + b/sinh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5900(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/cosh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5901(a, b, c, d, m, n, p, x):
|
|
return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/sinh(c + d*x))**p, x), x, x**n), x)
|
|
|
|
|
|
def replacement5902(a, b, c, d, m, n, p, x):
|
|
return Int(x**m*(a + b/cosh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5903(a, b, c, d, m, n, p, x):
|
|
return Int(x**m*(a + b/sinh(c + d*x**n))**p, x)
|
|
|
|
|
|
def replacement5904(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/cosh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5905(a, b, c, d, e, m, n, p, x):
|
|
return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/sinh(c + d*x**n))**p, x), x)
|
|
|
|
|
|
def replacement5906(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b/cosh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5907(a, b, e, m, p, u, x):
|
|
return Int((e*x)**m*(a + b/sinh(ExpandToSum(u, x)))**p, x)
|
|
|
|
|
|
def replacement5908(a, b, m, n, p, x):
|
|
return Dist((m - n + S(1))/(b*n*(p + S(-1))), Int(x**(m - n)*(S(1)/cosh(a + b*x**n))**(p + S(-1)), x), x) - Simp(x**(m - n + S(1))*(S(1)/cosh(a + b*x**n))**(p + S(-1))/(b*n*(p + S(-1))), x)
|
|
|
|
|
|
def replacement5909(a, b, m, n, p, x):
|
|
return Dist((m - n + S(1))/(b*n*(p + S(-1))), Int(x**(m - n)*(S(1)/sinh(a + b*x**n))**(p + S(-1)), x), x) - Simp(x**(m - n + S(1))*(S(1)/sinh(a + b*x**n))**(p + S(-1))/(b*n*(p + S(-1))), x)
|
|
|
|
|
|
def replacement5910(a, b, c, d, m, n, x):
|
|
return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*sinh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*sinh(a + b*x)**(n + S(1))/(b*(n + S(1))), x)
|
|
|
|
|
|
def replacement5911(a, b, c, d, m, n, x):
|
|
return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*cosh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*cosh(a + b*x)**(n + S(1))/(b*(n + S(1))), x)
|
|
|
|
|
|
def replacement5912(a, b, c, d, m, n, p, x):
|
|
return Int(ExpandTrigReduce((c + d*x)**m, sinh(a + b*x)**n*cosh(a + b*x)**p, x), x)
|
|
|
|
|
|
def replacement5913(a, b, c, d, m, n, p, x):
|
|
return Int((c + d*x)**m*sinh(a + b*x)**n*tanh(a + b*x)**(p + S(-2)), x) - Int((c + d*x)**m*sinh(a + b*x)**(n + S(-2))*tanh(a + b*x)**p, x)
|
|
|
|
|
|
def replacement5914(a, b, c, d, m, n, p, x):
|
|
return Int((c + d*x)**m*(S(1)/tanh(a + b*x))**p*cosh(a + b*x)**(n + S(-2)), x) + Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))*cosh(a + b*x)**n, x)
|
|
|
|
|
|
def replacement5915(a, b, c, d, m, n, p, x):
|
|
return Dist(d*m/(b*n), Int((c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**n/(b*n), x)
|
|
|
|
|
|
def replacement5916(a, b, c, d, m, n, p, x):
|
|
return Dist(d*m/(b*n), Int((c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**n/(b*n), x)
|
|
|
|
|
|
def replacement5917(a, b, c, d, m, n, x):
|
|
return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*tanh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*tanh(a + b*x)**(n + S(1))/(b*(n + S(1))), x)
|
|
|
|
|
|
def replacement5918(a, b, c, d, m, n, x):
|
|
return Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*(S(1)/tanh(a + b*x))**(n + S(1)), x), x) - Simp((c + d*x)**m*(S(1)/tanh(a + b*x))**(n + S(1))/(b*(n + S(1))), x)
|
|
|
|
|
|
def replacement5919(a, b, c, d, m, p, x):
|
|
return -Int((c + d*x)**m*tanh(a + b*x)**(p + S(-2))/cosh(a + b*x)**S(3), x) + Int((c + d*x)**m*tanh(a + b*x)**(p + S(-2))/cosh(a + b*x), x)
|
|
|
|
|
|
def replacement5920(a, b, c, d, m, n, p, x):
|
|
return Int((c + d*x)**m*(S(1)/cosh(a + b*x))**n*tanh(a + b*x)**(p + S(-2)), x) - Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(2))*tanh(a + b*x)**(p + S(-2)), x)
|
|
|
|
|
|
def replacement5921(a, b, c, d, m, p, x):
|
|
return Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))/sinh(a + b*x)**S(3), x) + Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))/sinh(a + b*x), x)
|
|
|
|
|
|
def replacement5922(a, b, c, d, m, n, p, x):
|
|
return Int((c + d*x)**m*(S(1)/sinh(a + b*x))**n*(S(1)/tanh(a + b*x))**(p + S(-2)), x) + Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(2))*(S(1)/tanh(a + b*x))**(p + S(-2)), x)
|
|
|
|
|
|
def With5923(a, b, c, d, m, n, p, x):
|
|
u = IntHide((S(1)/cosh(a + b*x))**n*tanh(a + b*x)**p, x)
|
|
return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x)
|
|
|
|
|
|
def With5924(a, b, c, d, m, n, p, x):
|
|
u = IntHide((S(1)/sinh(a + b*x))**n*(S(1)/tanh(a + b*x))**p, x)
|
|
return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x)
|
|
|
|
|
|
def replacement5925(a, b, c, d, m, n, x):
|
|
return Dist(S(2)**n, Int((c + d*x)**m*(S(1)/sinh(S(2)*a + S(2)*b*x))**n, x), x)
|
|
|
|
|
|
def With5926(a, b, c, d, m, n, p, x):
|
|
u = IntHide((S(1)/sinh(a + b*x))**n*(S(1)/cosh(a + b*x))**p, x)
|
|
return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x)
|
|
|
|
|
|
def replacement5927(F, G, m, n, p, u, v, w, x):
|
|
return Int(ExpandToSum(u, x)**m*F(ExpandToSum(v, x))**n*G(ExpandToSum(v, x))**p, x)
|
|
|
|
|
|
def replacement5928(a, b, c, d, e, f, m, n, x):
|
|
return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*sinh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*sinh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5929(a, b, c, d, e, f, m, n, x):
|
|
return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*cosh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*cosh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5930(a, b, c, d, e, f, m, n, x):
|
|
return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*tanh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*tanh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5931(a, b, c, d, e, f, m, n, x):
|
|
return Dist(f*m/(b*d*(n + S(1))), Int((a + b/tanh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/tanh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5932(a, b, c, d, e, f, m, n, x):
|
|
return Dist(f*m/(b*d*(n + S(1))), Int((a + b/cosh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/cosh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5933(a, b, c, d, e, f, m, n, x):
|
|
return Dist(f*m/(b*d*(n + S(1))), Int((a + b/sinh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/sinh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x)
|
|
|
|
|
|
def replacement5934(a, b, c, d, e, f, m, p, q, x):
|
|
return Int(ExpandTrigReduce((e + f*x)**m, sinh(a + b*x)**p*sinh(c + d*x)**q, x), x)
|
|
|
|
|
|
def replacement5935(a, b, c, d, e, f, m, p, q, x):
|
|
return Int(ExpandTrigReduce((e + f*x)**m, cosh(a + b*x)**p*cosh(c + d*x)**q, x), x)
|
|
|
|
|
|
def replacement5936(a, b, c, d, e, f, m, p, q, x):
|
|
return Int(ExpandTrigReduce((e + f*x)**m, sinh(a + b*x)**p*cosh(c + d*x)**q, x), x)
|
|
|
|
|
|
def replacement5937(F, G, a, b, c, d, e, f, m, p, q, x):
|
|
return Int(ExpandTrigExpand((e + f*x)**m*G(c + d*x)**q, F, c + d*x, p, b/d, x), x)
|
|
|
|
|
|
def replacement5938(F, a, b, c, d, e, x):
|
|
return Simp(F**(c*(a + b*x))*e*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x)
|
|
|
|
|
|
def replacement5939(F, a, b, c, d, e, x):
|
|
return Simp(F**(c*(a + b*x))*e*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x)
|
|
|
|
|
|
def replacement5940(F, a, b, c, d, e, n, x):
|
|
return -Dist(e**S(2)*n*(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**n/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) + Simp(F**(c*(a + b*x))*e*n*sinh(d + e*x)**(n + S(-1))*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5941(F, a, b, c, d, e, n, x):
|
|
return Dist(e**S(2)*n*(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*cosh(d + e*x)**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**n/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) + Simp(F**(c*(a + b*x))*e*n*sinh(d + e*x)*cosh(d + e*x)**(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5942(F, a, b, c, d, e, n, x):
|
|
return Simp(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(1))*cosh(d + e*x)/(e*(n + S(1))), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5943(F, a, b, c, d, e, n, x):
|
|
return -Simp(F**(c*(a + b*x))*sinh(d + e*x)*cosh(d + e*x)**(n + S(1))/(e*(n + S(1))), x) + Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5944(F, a, b, c, d, e, n, x):
|
|
return -Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(2))**S(2))/(e**S(2)*(n + S(1))*(n + S(2))), Int(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(2)), x), x) + Simp(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(1))*cosh(d + e*x)/(e*(n + S(1))), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5945(F, a, b, c, d, e, n, x):
|
|
return Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(2))**S(2))/(e**S(2)*(n + S(1))*(n + S(2))), Int(F**(c*(a + b*x))*cosh(d + e*x)**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*sinh(d + e*x)*cosh(d + e*x)**(n + S(1))/(e*(n + S(1))), x) + Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x)
|
|
|
|
|
|
def replacement5946(F, a, b, c, d, e, n, x):
|
|
return Dist((exp(S(2)*d + S(2)*e*x) + S(-1))**(-n)*exp(n*(d + e*x))*sinh(d + e*x)**n, Int(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**n*exp(-n*(d + e*x)), x), x)
|
|
|
|
|
|
def replacement5947(F, a, b, c, d, e, n, x):
|
|
return Dist((exp(S(2)*d + S(2)*e*x) + S(1))**(-n)*exp(n*(d + e*x))*cosh(d + e*x)**n, Int(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(1))**n*exp(-n*(d + e*x)), x), x)
|
|
|
|
|
|
def replacement5948(F, a, b, c, d, e, n, x):
|
|
return Int(ExpandIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**n*(exp(S(2)*d + S(2)*e*x) + S(1))**(-n), x), x)
|
|
|
|
|
|
def replacement5949(F, a, b, c, d, e, n, x):
|
|
return Int(ExpandIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**(-n)*(exp(S(2)*d + S(2)*e*x) + S(1))**n, x), x)
|
|
|
|
|
|
def replacement5950(F, a, b, c, d, e, n, x):
|
|
return Dist(e**S(2)*n*(n + S(1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**n*log(F)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) - Simp(F**(c*(a + b*x))*e*n*(S(1)/cosh(d + e*x))**(n + S(1))*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5951(F, a, b, c, d, e, n, x):
|
|
return -Dist(e**S(2)*n*(n + S(1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**n*log(F)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) - Simp(F**(c*(a + b*x))*e*n*(S(1)/sinh(d + e*x))**(n + S(1))*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x)
|
|
|
|
|
|
def replacement5952(F, a, b, c, d, e, n, x):
|
|
return Simp(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-1))*sinh(d + e*x)/(e*(n + S(-1))), x) + Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5953(F, a, b, c, d, e, n, x):
|
|
return -Simp(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-1))*cosh(d + e*x)/(e*(n + S(-1))), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5954(F, a, b, c, d, e, n, x):
|
|
return Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(-2))**S(2))/(e**S(2)*(n + S(-2))*(n + S(-1))), Int(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-2)), x), x) + Simp(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-1))*sinh(d + e*x)/(e*(n + S(-1))), x) + Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5955(F, a, b, c, d, e, n, x):
|
|
return -Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(-2))**S(2))/(e**S(2)*(n + S(-2))*(n + S(-1))), Int(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-1))*cosh(d + e*x)/(e*(n + S(-1))), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x)
|
|
|
|
|
|
def replacement5956(F, a, b, c, d, e, n, x):
|
|
return Simp(S(2)**n*F**(c*(a + b*x))*Hypergeometric2F1(n, b*c*log(F)/(S(2)*e) + n/S(2), b*c*log(F)/(S(2)*e) + n/S(2) + S(1), -exp(S(2)*d + S(2)*e*x))*exp(n*(d + e*x))/(b*c*log(F) + e*n), x)
|
|
|
|
|
|
def replacement5957(F, a, b, c, d, e, n, x):
|
|
return Simp((S(-2))**n*F**(c*(a + b*x))*Hypergeometric2F1(n, b*c*log(F)/(S(2)*e) + n/S(2), b*c*log(F)/(S(2)*e) + n/S(2) + S(1), exp(S(2)*d + S(2)*e*x))*exp(n*(d + e*x))/(b*c*log(F) + e*n), x)
|
|
|
|
|
|
def replacement5958(F, a, b, c, d, e, n, x):
|
|
return Dist((exp(S(2)*d + S(2)*e*x) + S(1))**n*(S(1)/cosh(d + e*x))**n*exp(-n*(d + e*x)), Int(SimplifyIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(1))**(-n)*exp(n*(d + e*x)), x), x), x)
|
|
|
|
|
|
def replacement5959(F, a, b, c, d, e, n, x):
|
|
return Dist((S(1) - exp(-S(2)*d - S(2)*e*x))**n*(S(1)/sinh(d + e*x))**n*exp(n*(d + e*x)), Int(SimplifyIntegrand(F**(c*(a + b*x))*(S(1) - exp(-S(2)*d - S(2)*e*x))**(-n)*exp(-n*(d + e*x)), x), x), x)
|
|
|
|
|
|
def replacement5960(F, a, b, c, d, e, f, g, n, x):
|
|
return Dist(S(2)**n*f**n, Int(F**(c*(a + b*x))*cosh(-Pi*f/(S(4)*g) + d/S(2) + e*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5961(F, a, b, c, d, e, f, g, n, x):
|
|
return Dist(S(2)**n*g**n, Int(F**(c*(a + b*x))*cosh(d/S(2) + e*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5962(F, a, b, c, d, e, f, g, n, x):
|
|
return Dist(S(2)**n*g**n, Int(F**(c*(a + b*x))*sinh(d/S(2) + e*x/S(2))**(S(2)*n), x), x)
|
|
|
|
|
|
def replacement5963(F, a, b, c, d, e, f, g, m, n, x):
|
|
return Dist(g**n, Int(F**(c*(a + b*x))*tanh(-Pi*f/(S(4)*g) + d/S(2) + e*x/S(2))**m, x), x)
|
|
|
|
|
|
def replacement5964(F, a, b, c, d, e, f, g, m, n, x):
|
|
return Dist(g**n, Int(F**(c*(a + b*x))*tanh(d/S(2) + e*x/S(2))**m, x), x)
|
|
|
|
|
|
def replacement5965(F, a, b, c, d, e, f, g, m, n, x):
|
|
return Dist(g**n, Int(F**(c*(a + b*x))*(S(1)/tanh(d/S(2) + e*x/S(2)))**m, x), x)
|
|
|
|
|
|
def replacement5966(F, a, b, c, d, e, f, g, h, i, x):
|
|
return Dist(S(2)*i, Int(F**(c*(a + b*x))*cosh(d + e*x)/(f + g*sinh(d + e*x)), x), x) + Int(F**(c*(a + b*x))*(h - i*cosh(d + e*x))/(f + g*sinh(d + e*x)), x)
|
|
|
|
|
|
def replacement5967(F, a, b, c, d, e, f, g, h, i, x):
|
|
return Dist(S(2)*i, Int(F**(c*(a + b*x))*sinh(d + e*x)/(f + g*cosh(d + e*x)), x), x) + Int(F**(c*(a + b*x))*(h - i*sinh(d + e*x))/(f + g*cosh(d + e*x)), x)
|
|
|
|
|
|
def replacement5968(F, G, c, n, u, v, x):
|
|
return Int(F**(c*ExpandToSum(u, x))*G(ExpandToSum(v, x))**n, x)
|
|
|
|
|
|
def With5969(F, a, b, c, d, e, m, n, x):
|
|
u = IntHide(F**(c*(a + b*x))*sinh(d + e*x)**n, x)
|
|
return -Dist(m, Int(u*x**(m + S(-1)), x), x) + Simp(u*x**m, x)
|
|
|
|
|
|
def With5970(F, a, b, c, d, e, m, n, x):
|
|
u = IntHide(F**(c*(a + b*x))*cosh(d + e*x)**n, x)
|
|
return -Dist(m, Int(u*x**(m + S(-1)), x), x) + Simp(u*x**m, x)
|
|
|
|
|
|
def replacement5971(F, a, b, c, d, e, f, g, m, n, x):
|
|
return Int(ExpandTrigReduce(F**(c*(a + b*x)), sinh(d + e*x)**m*cosh(f + g*x)**n, x), x)
|
|
|
|
|
|
def replacement5972(F, a, b, c, d, e, f, g, m, n, p, x):
|
|
return Int(ExpandTrigReduce(F**(c*(a + b*x))*x**p, sinh(d + e*x)**m*cosh(f + g*x)**n, x), x)
|
|
|
|
|
|
def replacement5973(F, G, H, a, b, c, d, e, m, n, x):
|
|
return Int(ExpandTrigToExp(F**(c*(a + b*x)), G(d + e*x)**m*H(d + e*x)**n, x), x)
|
|
|
|
|
|
def replacement5974(F, n, u, v, x):
|
|
return Int(ExpandTrigToExp(F**u, sinh(v)**n, x), x)
|
|
|
|
|
|
def replacement5975(F, n, u, v, x):
|
|
return Int(ExpandTrigToExp(F**u, cosh(v)**n, x), x)
|
|
|
|
|
|
def replacement5976(F, m, n, u, v, x):
|
|
return Int(ExpandTrigToExp(F**u, sinh(v)**m*cosh(v)**n, x), x)
|
|
|
|
|
|
def replacement5977(b, c, n, p, x):
|
|
return Int(((c*x**n)**b/S(2) - (c*x**n)**(-b)/S(2))**p, x)
|
|
|
|
|
|
def replacement5978(b, c, n, p, x):
|
|
return Int(((c*x**n)**b/S(2) + (c*x**n)**(-b)/S(2))**p, x)
|
|
|
|
|
|
def replacement5979(a, b, c, n, p, x):
|
|
return -Simp(x*(p + S(2))*sinh(a + b*log(c*x**n))**(p + S(2))/(p + S(1)), x) + Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x)
|
|
|
|
|
|
def replacement5980(a, b, c, n, p, x):
|
|
return Simp(x*(p + S(2))*cosh(a + b*log(c*x**n))**(p + S(2))/(p + S(1)), x) - Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x)
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def replacement5981(a, b, c, n, x):
|
|
return Dist(x*sqrt(sinh(a + b*log(c*x**n)))/sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(-1)), Int(sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(-1))/x, x), x)
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|
|
|
|
|
def replacement5982(a, b, c, n, x):
|
|
return Dist(x*sqrt(cosh(a + b*log(c*x**n)))/sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(1)), Int(sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(1))/x, x), x)
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|
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|
|
|
def replacement5983(a, b, c, n, p, x):
|
|
return Int(ExpandIntegrand(((c*x**n)**(S(1)/(n*p))*exp(a*b*n*p)/(S(2)*b*n*p) - (c*x**n)**(-S(1)/(n*p))*exp(-a*b*n*p)/(S(2)*b*n*p))**p, x), x)
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|
|
|
|
|
def replacement5984(a, b, c, n, p, x):
|
|
return Int(ExpandIntegrand(((c*x**n)**(S(1)/(n*p))*exp(a*b*n*p)/S(2) + (c*x**n)**(-S(1)/(n*p))*exp(-a*b*n*p)/S(2))**p, x), x)
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|
|
|
|
|
def replacement5985(a, b, c, n, x):
|
|
return -Simp(x*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) + Simp(b*n*x*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x)
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|
|
def replacement5986(a, b, c, n, x):
|
|
return -Simp(x*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) + Simp(b*n*x*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x)
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|
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def replacement5987(a, b, c, n, p, x):
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|
return -Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int(sinh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x*sinh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) + Simp(b*n*p*x*sinh(a + b*log(c*x**n))**(p + S(-1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x)
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|
|
def replacement5988(a, b, c, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int(cosh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x*cosh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) + Simp(b*n*p*x*sinh(a + b*log(c*x**n))*cosh(a + b*log(c*x**n))**(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x)
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|
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|
|
def replacement5989(a, b, c, n, p, x):
|
|
return -Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(sinh(a + b*log(c*x**n))**(p + S(2)), x), x) - Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) + Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x)
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|
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def replacement5990(a, b, c, n, p, x):
|
|
return Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(cosh(a + b*log(c*x**n))**(p + S(2)), x), x) + Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) - Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x)
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|
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|
|
def replacement5991(a, b, c, n, p, x):
|
|
return Simp(x*(S(2) - S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) - (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + S(1))/(S(2)*b*n), S(1) - (b*n*p + S(1))/(S(2)*b*n), (c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + S(1)), x)
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|
|
def replacement5992(a, b, c, n, p, x):
|
|
return Simp(x*(S(2) + S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) + (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + S(1))/(S(2)*b*n), S(1) - (b*n*p + S(1))/(S(2)*b*n), -(c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + S(1)), x)
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|
|
|
def replacement5993(a, b, c, m, n, p, x):
|
|
return -Simp(x**(m + S(1))*(p + S(2))*sinh(a + b*log(c*x**n))**(p + S(2))/((m + S(1))*(p + S(1))), x) + Simp(x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x)
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|
|
def replacement5994(a, b, c, m, n, p, x):
|
|
return Simp(x**(m + S(1))*(p + S(2))*cosh(a + b*log(c*x**n))**(p + S(2))/((m + S(1))*(p + S(1))), x) - Simp(x**(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x)
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|
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|
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def replacement5995(a, b, c, m, n, p, x):
|
|
return Dist(S(2)**(-p), Int(ExpandIntegrand(x**m*((c*x**n)**((m + S(1))/(n*p))*(m + S(1))*exp(a*b*n*p/(m + S(1)))/(b*n*p) - (c*x**n)**(-(m + S(1))/(n*p))*(m + S(1))*exp(-a*b*n*p/(m + S(1)))/(b*n*p))**p, x), x), x)
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|
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|
|
def replacement5996(a, b, c, m, n, p, x):
|
|
return Dist(S(2)**(-p), Int(ExpandIntegrand(x**m*((c*x**n)**((m + S(1))/(n*p))*exp(a*b*n*p/(m + S(1))) + (c*x**n)**(-(m + S(1))/(n*p))*exp(-a*b*n*p/(m + S(1))))**p, x), x), x)
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|
|
|
|
|
def replacement5997(a, b, c, m, n, x):
|
|
return -Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*x**(m + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x)
|
|
|
|
|
|
def replacement5998(a, b, c, m, n, x):
|
|
return -Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*x**(m + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x)
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|
|
|
|
|
def replacement5999(a, b, c, m, n, p, x):
|
|
return -Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*sinh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*p*x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(-1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x)
|
|
|
|
|
|
def replacement6000(a, b, c, m, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*cosh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*p*x**(m + S(1))*sinh(a + b*log(c*x**n))*cosh(a + b*log(c*x**n))**(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x)
|
|
|
|
|
|
def replacement6001(a, b, c, m, n, p, x):
|
|
return -Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**m*sinh(a + b*log(c*x**n))**(p + S(2)), x), x) + Simp(x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x) - Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x)
|
|
|
|
|
|
def replacement6002(a, b, c, m, n, p, x):
|
|
return Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**m*cosh(a + b*log(c*x**n))**(p + S(2)), x), x) - Simp(x**(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x) + Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x)
|
|
|
|
|
|
def replacement6003(a, b, c, m, n, p, x):
|
|
return Simp(x**(m + S(1))*(S(2) - S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) - (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + m + S(1))/(S(2)*b*n), S(1) - (b*n*p + m + S(1))/(S(2)*b*n), (c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + m + S(1)), x)
|
|
|
|
|
|
def replacement6004(a, b, c, m, n, p, x):
|
|
return Simp(x**(m + S(1))*(S(2) + S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) + (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + m + S(1))/(S(2)*b*n), S(1) - (b*n*p + m + S(1))/(S(2)*b*n), -(c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + m + S(1)), x)
|
|
|
|
|
|
def replacement6005(b, c, n, p, x):
|
|
return Dist(S(2)**p, Int(((c*x**n)**b/((c*x**n)**(S(2)*b) + S(1)))**p, x), x)
|
|
|
|
|
|
def replacement6006(b, c, n, p, x):
|
|
return Dist(S(2)**p, Int(((c*x**n)**b/((c*x**n)**(S(2)*b) + S(-1)))**p, x), x)
|
|
|
|
|
|
def replacement6007(a, b, c, n, x):
|
|
return Dist(S(2)*exp(-a*b*n), Int((c*x**n)**(S(1)/n)/((c*x**n)**(S(2)/n) + exp(-S(2)*a*b*n)), x), x)
|
|
|
|
|
|
def replacement6008(a, b, c, n, x):
|
|
return Dist(-S(2)*b*n*exp(-a*b*n), Int((c*x**n)**(S(1)/n)/(-(c*x**n)**(S(2)/n) + exp(-S(2)*a*b*n)), x), x)
|
|
|
|
|
|
def replacement6009(a, b, c, n, p, x):
|
|
return Simp(x*(p + S(-2))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(p + S(-1)), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x)
|
|
|
|
|
|
def replacement6010(a, b, c, n, p, x):
|
|
return -Simp(x*(p + S(-2))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(p + S(-1)), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x)
|
|
|
|
|
|
def replacement6011(a, b, c, n, p, x):
|
|
return Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int((S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2)), x), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x)
|
|
|
|
|
|
def replacement6012(a, b, c, n, p, x):
|
|
return -Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int((S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2)), x), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x)
|
|
|
|
|
|
def replacement6013(a, b, c, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int((S(1)/cosh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) - Simp(b*n*p*x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x)
|
|
|
|
|
|
def replacement6014(a, b, c, n, p, x):
|
|
return -Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int((S(1)/sinh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) - Simp(b*n*p*x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x)
|
|
|
|
|
|
def replacement6015(a, b, c, n, p, x):
|
|
return Simp(S(2)**p*x*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1)))**p*((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + S(1))/(S(2)*b*n), S(1) + (b*n*p + S(1))/(S(2)*b*n), -(c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + S(1)), x)
|
|
|
|
|
|
def replacement6016(a, b, c, n, p, x):
|
|
return Simp(x*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(-1)))**p*(-S(2)*(c*x**n)**(S(2)*b)*exp(S(2)*a) + S(2))**p*Hypergeometric2F1(p, (b*n*p + S(1))/(S(2)*b*n), S(1) + (b*n*p + S(1))/(S(2)*b*n), (c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + S(1)), x)
|
|
|
|
|
|
def replacement6017(b, c, m, n, p, x):
|
|
return Dist(S(2)**p, Int(x**m*((c*x**n)**b/((c*x**n)**(S(2)*b) + S(1)))**p, x), x)
|
|
|
|
|
|
def replacement6018(b, c, m, n, p, x):
|
|
return Dist(S(2)**p, Int(x**m*((c*x**n)**b/((c*x**n)**(S(2)*b) + S(-1)))**p, x), x)
|
|
|
|
|
|
def replacement6019(a, b, c, m, n, x):
|
|
return Dist(S(2)*exp(-a*b*n/(m + S(1))), Int(x**m*(c*x**n)**((m + S(1))/n)/((c*x**n)**(S(2)*(m + S(1))/n) + exp(-S(2)*a*b*n/(m + S(1)))), x), x)
|
|
|
|
|
|
def replacement6020(a, b, c, m, n, x):
|
|
return Dist(-S(2)*b*n*exp(-a*b*n/(m + S(1)))/(m + S(1)), Int(x**m*(c*x**n)**((m + S(1))/n)/(-(c*x**n)**(S(2)*(m + S(1))/n) + exp(-S(2)*a*b*n/(m + S(1)))), x), x)
|
|
|
|
|
|
def replacement6021(a, b, c, m, n, p, x):
|
|
return Simp(x**(m + S(1))*(p + S(-2))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/((m + S(1))*(p + S(-1))), x) + Simp(x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x)
|
|
|
|
|
|
def replacement6022(a, b, c, m, n, p, x):
|
|
return -Simp(x**(m + S(1))*(p + S(-2))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/((m + S(1))*(p + S(-1))), x) - Simp(x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x)
|
|
|
|
|
|
def replacement6023(a, b, c, m, n, p, x):
|
|
return Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int(x**m*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2)), x), x) + Simp(x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x) + Simp(x**(m + S(1))*(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x)
|
|
|
|
|
|
def replacement6024(a, b, c, m, n, p, x):
|
|
return -Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int(x**m*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x)
|
|
|
|
|
|
def replacement6025(a, b, c, m, n, p, x):
|
|
return Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) - Simp(b*n*p*x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x)
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|
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|
|
|
def replacement6026(a, b, c, m, n, p, x):
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|
return -Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) - Simp(b*n*p*x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x)
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|
|
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|
|
def replacement6027(a, b, c, m, n, p, x):
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|
return Simp(S(2)**p*x**(m + S(1))*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1)))**p*((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + m + S(1))/(S(2)*b*n), S(1) + (b*n*p + m + S(1))/(S(2)*b*n), -(c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + m + S(1)), x)
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|
|
|
|
|
def replacement6028(a, b, c, m, n, p, x):
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|
return Simp(S(2)**p*x**(m + S(1))*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(-1)))**p*(-(c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + m + S(1))/(S(2)*b*n), S(1) + (b*n*p + m + S(1))/(S(2)*b*n), (c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + m + S(1)), x)
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|
|
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|
|
def replacement6029(a, b, p, x):
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|
return -Dist(p, Int(log(b*x)**(p + S(-1))*sinh(a*x*log(b*x)**p), x), x) + Simp(cosh(a*x*log(b*x)**p)/a, x)
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|
|
|
|
def replacement6030(a, b, p, x):
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|
return -Dist(p, Int(log(b*x)**(p + S(-1))*cosh(a*x*log(b*x)**p), x), x) + Simp(sinh(a*x*log(b*x)**p)/a, x)
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|
|
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def replacement6031(a, b, n, p, x):
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|
return -Dist(p/n, Int(log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) + Dist((n + S(-1))/(a*n), Int(x**(-n)*cosh(a*x**n*log(b*x)**p), x), x) + Simp(x**(S(1) - n)*cosh(a*x**n*log(b*x)**p)/(a*n), x)
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|
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|
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def replacement6032(a, b, n, p, x):
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|
return -Dist(p/n, Int(log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) + Dist((n + S(-1))/(a*n), Int(x**(-n)*sinh(a*x**n*log(b*x)**p), x), x) + Simp(x**(S(1) - n)*sinh(a*x**n*log(b*x)**p)/(a*n), x)
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|
|
|
def replacement6033(a, b, m, n, p, x):
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|
return -Dist(p/n, Int(x**(n + S(-1))*log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) - Simp(cosh(a*x**n*log(b*x)**p)/(a*n), x)
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|
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def replacement6034(a, b, m, n, p, x):
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|
return -Dist(p/n, Int(x**(n + S(-1))*log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) + Simp(sinh(a*x**n*log(b*x)**p)/(a*n), x)
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|
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|
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def replacement6035(a, b, m, n, p, x):
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|
return -Dist(p/n, Int(x**m*log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) - Dist((m - n + S(1))/(a*n), Int(x**(m - n)*cosh(a*x**n*log(b*x)**p), x), x) + Simp(x**(m - n + S(1))*cosh(a*x**n*log(b*x)**p)/(a*n), x)
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|
|
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|
def replacement6036(a, b, m, n, p, x):
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|
return -Dist(p/n, Int(x**m*log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) - Dist((m - n + S(1))/(a*n), Int(x**(m - n)*sinh(a*x**n*log(b*x)**p), x), x) + Simp(x**(m - n + S(1))*sinh(a*x**n*log(b*x)**p)/(a*n), x)
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|
|
|
|
|
def replacement6037(a, c, d, n, x):
|
|
return -Dist(S(1)/d, Subst(Int(sinh(a*x)**n/x**S(2), x), x, S(1)/(c + d*x)), x)
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|
|
|
|
|
def replacement6038(a, c, d, n, x):
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|
return -Dist(S(1)/d, Subst(Int(cosh(a*x)**n/x**S(2), x), x, S(1)/(c + d*x)), x)
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|
|
|
|
|
def replacement6039(a, b, c, d, e, n, x):
|
|
return -Dist(S(1)/d, Subst(Int(sinh(b*e/d - e*x*(-a*d + b*c)/d)**n/x**S(2), x), x, S(1)/(c + d*x)), x)
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|
|
|
|
|
def replacement6040(a, b, c, d, e, n, x):
|
|
return -Dist(S(1)/d, Subst(Int(cosh(b*e/d - e*x*(-a*d + b*c)/d)**n/x**S(2), x), x, S(1)/(c + d*x)), x)
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|
|
|
|
|
def With6041(n, u, x):
|
|
lst = QuotientOfLinearsParts(u, x)
|
|
return Int(sinh((x*Part(lst, S(2)) + Part(lst, S(1)))/(x*Part(lst, S(4)) + Part(lst, S(3))))**n, x)
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|
|
|
|
|
def With6042(n, u, x):
|
|
lst = QuotientOfLinearsParts(u, x)
|
|
return Int(cosh((x*Part(lst, S(2)) + Part(lst, S(1)))/(x*Part(lst, S(4)) + Part(lst, S(3))))**n, x)
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|
|
|
|
|
def replacement6043(p, q, u, v, w, x):
|
|
return Int(u*sinh(v)**(p + q), x)
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|
|
|
|
|
def replacement6044(p, q, u, v, w, x):
|
|
return Int(u*cosh(v)**(p + q), x)
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|
|
|
|
|
def replacement6045(p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(sinh(v)**p*sinh(w)**q, x), x)
|
|
|
|
|
|
def replacement6046(p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(cosh(v)**p*cosh(w)**q, x), x)
|
|
|
|
|
|
def replacement6047(m, p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(x**m, sinh(v)**p*sinh(w)**q, x), x)
|
|
|
|
|
|
def replacement6048(m, p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(x**m, cosh(v)**p*cosh(w)**q, x), x)
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|
|
|
|
|
def replacement6049(p, u, v, w, x):
|
|
return Dist(S(2)**(-p), Int(u*sinh(S(2)*v)**p, x), x)
|
|
|
|
|
|
def replacement6050(p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(sinh(v)**p*cosh(w)**q, x), x)
|
|
|
|
|
|
def replacement6051(m, p, q, v, w, x):
|
|
return Int(ExpandTrigReduce(x**m, sinh(v)**p*cosh(w)**q, x), x)
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|
|
|
|
|
def replacement6052(n, v, w, x):
|
|
return -Dist(cosh(v - w), Int(tanh(w)**(n + S(-1))/cosh(w), x), x) + Int(cosh(v)*tanh(w)**(n + S(-1)), x)
|
|
|
|
|
|
def replacement6053(n, v, w, x):
|
|
return Dist(cosh(v - w), Int((S(1)/tanh(w))**(n + S(-1))/sinh(w), x), x) + Int((S(1)/tanh(w))**(n + S(-1))*sinh(v), x)
|
|
|
|
|
|
def replacement6054(n, v, w, x):
|
|
return Dist(sinh(v - w), Int((S(1)/tanh(w))**(n + S(-1))/sinh(w), x), x) + Int((S(1)/tanh(w))**(n + S(-1))*cosh(v), x)
|
|
|
|
|
|
def replacement6055(n, v, w, x):
|
|
return -Dist(sinh(v - w), Int(tanh(w)**(n + S(-1))/cosh(w), x), x) + Int(sinh(v)*tanh(w)**(n + S(-1)), x)
|
|
|
|
|
|
def replacement6056(n, v, w, x):
|
|
return Dist(sinh(v - w), Int((S(1)/cosh(w))**(n + S(-1)), x), x) + Dist(cosh(v - w), Int((S(1)/cosh(w))**(n + S(-1))*tanh(w), x), x)
|
|
|
|
|
|
def replacement6057(n, v, w, x):
|
|
return Dist(sinh(v - w), Int((S(1)/sinh(w))**(n + S(-1)), x), x) + Dist(cosh(v - w), Int((S(1)/sinh(w))**(n + S(-1))/tanh(w), x), x)
|
|
|
|
|
|
def replacement6058(n, v, w, x):
|
|
return Dist(sinh(v - w), Int((S(1)/sinh(w))**(n + S(-1))/tanh(w), x), x) + Dist(cosh(v - w), Int((S(1)/sinh(w))**(n + S(-1)), x), x)
|
|
|
|
|
|
def replacement6059(n, v, w, x):
|
|
return Dist(sinh(v - w), Int((S(1)/cosh(w))**(n + S(-1))*tanh(w), x), x) + Dist(cosh(v - w), Int((S(1)/cosh(w))**(n + S(-1)), x), x)
|
|
|
|
|
|
def replacement6060(a, b, c, d, e, f, m, n, x):
|
|
return Int((a + b*sinh(S(2)*c + S(2)*d*x)/S(2))**n*(e + f*x)**m, x)
|
|
|
|
|
|
def replacement6061(a, b, c, d, m, n, x):
|
|
return Dist(S(2)**(-n), Int(x**m*(S(2)*a + b*cosh(S(2)*c + S(2)*d*x) - b)**n, x), x)
|
|
|
|
|
|
def replacement6062(a, b, c, d, m, n, x):
|
|
return Dist(S(2)**(-n), Int(x**m*(S(2)*a + b*cosh(S(2)*c + S(2)*d*x) + b)**n, x), x)
|
|
|
|
|
|
def replacement6063(a, b, c, d, e, f, m, n, p, x):
|
|
return Dist(d**(-m + S(-1)), Subst(Int((-c*f + d*e + f*x)**m*sinh(a + b*x**n)**p, x), x, c + d*x), x)
|
|
|
|
|
|
def replacement6064(a, b, c, d, e, f, m, n, p, x):
|
|
return Dist(d**(-m + S(-1)), Subst(Int((-c*f + d*e + f*x)**m*cosh(a + b*x**n)**p, x), x, c + d*x), x)
|
|
|
|
|
|
def replacement6065(a, b, c, d, e, f, g, m, x):
|
|
return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x)
|
|
|
|
|
|
def replacement6066(b, c, d, e, f, g, m, x):
|
|
return Dist(S(2), Int((f + g*x)**m/(b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x)
|
|
|
|
|
|
def replacement6067(a, b, c, d, e, f, g, m, x):
|
|
return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x)
|
|
|
|
|
|
def replacement6068(b, c, d, e, f, g, m, x):
|
|
return Dist(S(2), Int((f + g*x)**m/(b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x)
|
|
|
|
|
|
def replacement6069(a, b, c, d, e, f, g, m, x):
|
|
return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x)
|
|
|
|
|
|
def replacement6070(a, b, c, d, e, f, m, x):
|
|
return Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) - Rt(a**S(2) + b**S(2), S(2))), x) + Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) + Rt(a**S(2) + b**S(2), S(2))), x) - Simp((e + f*x)**(m + S(1))/(b*f*(m + S(1))), x)
|
|
|
|
|
|
def replacement6071(a, b, c, d, e, f, m, x):
|
|
return Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) - Rt(a**S(2) - b**S(2), S(2))), x) + Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) + Rt(a**S(2) - b**S(2), S(2))), x) - Simp((e + f*x)**(m + S(1))/(b*f*(m + S(1))), x)
|
|
|
|
|
|
def replacement6072(a, b, c, d, e, f, m, n, x):
|
|
return Dist(S(1)/a, Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2)), x), x) + Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)*cosh(c + d*x)**(n + S(-2)), x), x)
|
|
|
|
|
|
def replacement6073(a, b, c, d, e, f, m, n, x):
|
|
return Dist(S(1)/a, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2)), x), x) + Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))*cosh(c + d*x), x), x)
|
|
|
|
|
|
def replacement6074(a, b, c, d, e, f, m, n, x):
|
|
return Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)*cosh(c + d*x)**(n + S(-2)), x), x) - Dist(a/b**S(2), Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2)), x), x) + Dist((a**S(2) + b**S(2))/b**S(2), Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2))/(a + b*sinh(c + d*x)), x), x)
|
|
|
|
|
|
def replacement6075(a, b, c, d, e, f, m, n, x):
|
|
return Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))*cosh(c + d*x), x), x) - Dist(a/b**S(2), Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2)), x), x) + Dist((a**S(2) - b**S(2))/b**S(2), Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))/(a + b*cosh(c + d*x)), x), x)
|
|
|
|
|
|
def replacement6076(A, B, a, b, c, d, e, f, x):
|
|
return -Dist(B*f/(a*d), Int(cosh(c + d*x)/(a + b*sinh(c + d*x)), x), x) + Simp(B*(e + f*x)*cosh(c + d*x)/(a*d*(a + b*sinh(c + d*x))), x)
|
|
|
|
|
|
def replacement6077(A, B, a, b, c, d, e, f, x):
|
|
return -Dist(B*f/(a*d), Int(sinh(c + d*x)/(a + b*cosh(c + d*x)), x), x) + Simp(B*(e + f*x)*sinh(c + d*x)/(a*d*(a + b*cosh(c + d*x))), x)
|
|
|
|
|
|
def replacement6078(a, b, m, n, v, x):
|
|
return Int((a*cosh(v) + b*sinh(v))**n, x)
|
|
|
|
|
|
def replacement6079(a, b, m, n, v, x):
|
|
return Int((a*sinh(v) + b*cosh(v))**n, x)
|
|
|
|
|
|
def replacement6080(a, b, c, d, m, n, u, x):
|
|
return Int(ExpandTrigReduce(u, sinh(a + b*x)**m*sinh(c + d*x)**n, x), x)
|
|
|
|
|
|
def replacement6081(a, b, c, d, m, n, u, x):
|
|
return Int(ExpandTrigReduce(u, cosh(a + b*x)**m*cosh(c + d*x)**n, x), x)
|
|
|
|
|
|
def replacement6082(a, b, c, d, x):
|
|
return Dist(S(1)/sinh((-a*d + b*c)/b), Int(tanh(c + d*x), x), x) - Dist(S(1)/sinh((-a*d + b*c)/d), Int(tanh(a + b*x), x), x)
|
|
|
|
|
|
def replacement6083(a, b, c, d, x):
|
|
return Dist(S(1)/sinh((-a*d + b*c)/b), Int(S(1)/tanh(a + b*x), x), x) - Dist(S(1)/sinh((-a*d + b*c)/d), Int(S(1)/tanh(c + d*x), x), x)
|
|
|
|
|
|
def replacement6084(a, b, c, d, x):
|
|
return -Dist(b*cosh((-a*d + b*c)/d)/d, Int(S(1)/(cosh(a + b*x)*cosh(c + d*x)), x), x) + Simp(b*x/d, x)
|
|
|
|
|
|
def replacement6085(a, b, c, d, x):
|
|
return Dist(cosh((-a*d + b*c)/d), Int(S(1)/(sinh(a + b*x)*sinh(c + d*x)), x), x) + Simp(b*x/d, x)
|
|
|
|
|
|
def replacement6086(a, b, n, u, v, x):
|
|
return Int(u*(a*exp(a*v/b))**n, x)
|