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

A power of x times a function of one logarithm of a monomial, x^m G(ln(c x^n)),
under t = ln(c x^n): dx = x dt/n, and x^(m + 1) is
K e^((m + 1) t/n) with K = x^(m + 1) (c x^n)^(-(m + 1)/n), whose derivative
is 0 wherever it is defined. So the answer is K/n times the integral of
e^((m + 1) t/n) G(t) at t = ln(c x^n), an antiderivative on the whole of
the real line where the integrand is real -- for an even n that includes negative
x, where ln(c x^n) is not ln(c) + n ln(x). A power of a monomial,
(e x)^p, is x^p times a factor of the same kind. What by parts leaves of
(e x)^m Si(d (a + b ln(c x^n))) is this, with G(t) a sine over a linear in
t. Rubi's answers to 8.3 to 8.5 are written in exactly this K.
https://github.com/asc-community/AngouriMath/issues/1501