AngouriMath
SolveByTakingTheHyperbolicCosineSquaredOutOfAPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A fractional power of a rational function of sinh(y) and cosh(y) whose
numerator hascosh(y)^2 as a factor -- with cosh(y)^2 written
1 + sinh(y)^2 -- taken out of the power: (cosh(y)^2 A/B)^p is
cosh(y)^(2p) A^p B^(-p) times a constant on every interval where both are
continuous.(cosh(x) coth(x))^(3/2) and (csch(x) + sinh(x))^(3/2) are both
(cosh(x)^2/sinh(x))^(3/2) , which is cosh(x)^3 sinh(x)^(-3/2) on
x > 0 , odd in the hyperbolic cosine.
https://github.com/asc-community/AngouriMath/issues/233
numerator has
continuous.
https://github.com/asc-community/AngouriMath/issues/233
Remarks
Rubi's six in 6.7.1 were declined: the radicand is a quotient, and
SolveByBiochesOddHyperbolicSubstitution(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) reads the radicands that are
polynomials. The constant is not written: each power as written over its form apart is a
quotient whose logarithmic derivative is zero, so it is constant wherever it is
continuous, and the answer is the antiderivative of the rewritten integrand times their
product. Only where an odd power of the sine is left beside it.
SolveByBiochesOddHyperbolicSubstitution(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) reads the radicands that are
polynomials. The constant is not written: each power as written over its form apart is a
quotient whose logarithmic derivative is zero, so it is constant wherever it is
continuous, and the answer is the antiderivative of the rewritten integrand times their
product. Only where an odd power of the sine is left beside it.
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