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

A power of x times a half-odd power of a logarithm, x^p F^n with F =
ln x or A + B ln(c x^r) and 2n odd, onto the Gaussian's moments.
With t = sqrt(F) and F' = s/x, dx = 2 x t dt/s, and
x^(p + 1) e^(-(p + 1) F/s) is a constant, so the integral is that constant times
2/s times the integral of t^(2n + 1) e^((p + 1) t^2/s): an even moment of
the Gaussian, which the table answers. At p = -1 it is
F^(n + 1)/(s (n + 1)). Rubi's 3.1.2, (d x)^m (a + b ln(c x^n))^p for a
half-odd p.
https://github.com/asc-community/AngouriMath/issues/1501