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

 Method (no overloads)

Summary

A power that is not whole of a constant times a whole power of something of x,
(c S^k)^p for a whole k past 1, as K S^(k p), with
K = c^q (c S^k)^r/S^(k r) for the whole part q of p and the rest
r: Rubi's 1.3.2 x^m (c (a + b x^2)^2)^(3/2) is K x^m (a + b x^2)^3,
a polynomial, and was declined.

Remarks

K is constant on every interval where S is not zero: its logarithmic
derivative is r (k S'/S - k S'/S). So it goes in front of the integral, and over it
for a factor below the bar, as the factor of
SolveByTakingAPowerOfXOutOfAFractionalPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) does. A whole power of the
constant times the power distributes exactly, which is why only the rest of p is
in K. Only factors of the integrand, where K is a factor of the whole; only
something of x by arithmetic, since a power of a function is the rules' for that function,
which write its sign; and at the top only, where the answer is the caller's.
https://github.com/asc-community/AngouriMath/issues/718

























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