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

A rational function over a whole power of a symbolic quadratic, beside at most one
linear to a whole power, with the power of the quadratic lowered one at a time rather
than the quadratic taken apart: the linear comes off first, as
N/(L^j Q^n) = N(p)/(Q(p)^n L^j) + M/(L^(j - 1) Q^n) at its root p, and
what is left over Q^k is S/Q^(k - 1) + (alpha Q' + beta)/Q^k, whose second
part is -alpha/((k - 1) Q^(k - 1)) and the recurrence
integral 1/Q^k = (2 c x + b)/((k - 1) D Q^(k - 1)) + 2 c (2 k - 3)/((k - 1) D) integral 1/Q^(k - 1) with D = 4 a c - b^2, down to the first power, which is the integrator's.