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

A polynomial in sines and cosines of one linear, times a polynomial, over a whole power
of a linear: P(x) T(sin(a + b x), cos(a + b x))/(e + f x)^n, onto the sine and
cosine integrals. Each monomial sin^s cos^c of T is a sum of sines and
cosines of multiples of the argument, and under u = e + f x, with
alpha = a - b e/f and k = b/f, sin(j (a + b x)) is
sin(j alpha) cos(j k u) + cos(j alpha) sin(j k u) and the cosine likewise, so every
term is u^m sin(q u) or u^m cos(q u): elementary for m >= 0,
Si(q u) and Ci(q u) for m = -1, which is their definition, and below
that by parts toward them. The constant term an even power leaves is a power of u alone. Several linears below the bar are split into partial fractions over them, each
term the question for one; and an argument a + b x^r beside a power of x is
the same question under u = x^r, where x^p dx is u^((p + 1)/r - 1) du/r.
Rubi's 4.1.10, (c + d x)^m (a + b sin(e + f x))^n, 4.1.11,
sin(c + d x)/(x^m (a + b x)^n), and 4.1.12, (e x)^m (a + b sin(c + d x^n))^p,
with m negative.
https://github.com/asc-community/AngouriMath/issues/1501