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

A power of x times an exponential of a quadratic in a logarithm, x^p G^(Q(L)) with
L = ln(c x^r) and Q a quadratic with a square term, onto the
Gaussian. With t = L and L' = s/x, dx = x dt/s, and
x^(p + 1) e^(-(p + 1) L/s) is a constant, so the integral is that constant over
s times the integral of e^(Q(t) ln G + (p + 1) t/s): the Gaussian with a
linear term, which the table answers. A polynomial beside it is summed a power at a time,
and the logarithm of a power of a linear is the same question under u = d + e x.
Rubi's 2.3, F^(f (a + b ln(c (d + e x)^n))^2) (g + h x)^m and
F^(f (a + b ln(c (d + e x)^n)^2)) (g + h x)^m.
https://github.com/asc-community/AngouriMath/issues/1501