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

 Method (no overloads)

Summary

A power of x that is not whole beside whole powers of two binomials in x^n or
more, x^q R(x^n) with R over (a + b x^n)^j (c + d x^n)^k, split into
partial fractions in w = x^n, with x^r for q = r + n m, 0 < r < n,
kept beside each term: Rubi's x^(9/2)/((a + b x^2) (c + d x^2)^2) is
sqrt(x) times w^2/((a + b w) (c + d w)^2) written apart, three binomial
differentials.

Remarks

The split is over the binomials as linears in w, so its coefficients are rational in the
symbols, and it is checked at sampled points before it is used; each term is a constant
times x^(r + n i)/(a + b x^n)^l, which the rules for one binomial answer in a tenth
of a second. These were declined past the budget: the polynomial term makes each
binomial monic, and the substitution u = sqrt(x) and the partial fractions after
it went on to take u^10/((a + b u^4) (c + d u^4)^2) apart over the fourth roots of
both. With a symbol only, at the question asked, before the polynomial term, and with one of
the binomials below the bar past its first power: over two first powers the routes as
written answer. A whole power of x is a rational function, and the rational integrator's.
https://github.com/asc-community/AngouriMath/issues/233

























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