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SolveAProductOfPowersOfTheVariable(AngouriMath.Entity,AngouriMath.Entity.Variable)

Method (no overloads)

Summary

A product of powers of the variable and of constant multiples of it,
(c x)^m (d x)^k x^n times a constant, with at least one written multiple:
(c x)^m (d x)^k x^(n+1)/(m + k + n + 1), and the logarithm where the sum of
the exponents is minus one.

Remarks

The written power is kept as it is, which is what makes this exact: for every
x but zero, d/dx (c x)^m is m (c x)^m / x, since
(c x)^(m-1) is (c x)^m / (c x) whatever the branch, and each factor
contributes its exponent over x. Opening (c x)^m into c^m x^m would need c or x positive. Rubi's (e x)^m (a + b x^n)^p (c + d x^n)^q with symbolic m and n, expanded, is a sum of these and was declined
term by term, the power rule reading x^p and nothing else.
A power of x alone is left to the power rule, which answers it as before.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

SolveAProductOfPowersOfTheVariable​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

SolveAProductOfPowersOfTheVariable(AngouriMath.Entity,AngouriMath.Entity.Variable)