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SolveByTakingTheWholePowersOutOfAPowerOfAProduct(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)

Method (no overloads)

Summary

A power of a product with a factor under a whole power, that power taken out:
(c R f^n)^r is K f^(n r) R^r, where K = (c R f^n)^r/(f^(n r) R^r) and
c is free of x. The logarithmic derivatives of both sides are
r (R'/R + n f'/f), so K is
constant wherever it is defined, and it stands in front of the answer the way Rubi
writes (c sin(a + b x)^3)^(1/3) csc(a + b x) in front of its.

Remarks

(c sin(a + b x)^3)^(1/3)/x, sqrt((x^2 - 1)^2/(x (1 + x^2)))/(1 + x^2) and
1/sqrt((a^2 + x^2)^3) were declined: nothing reads a function under a root of its
own power. With the power taken out each is K times an integrand the chain
answers. After every other rule, and at the question asked only.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

SolveByTakingTheWholePowersOutOfAPowerOfAProduct​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

SolveByTakingTheWholePowersOutOfAPowerOfAProduct(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)