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

 Method (no overloads)

Summary

N/(L^k B) for a linear L = g + h x other than x, beside a block B with a symbol in it, past the second degree, that does not vanish at the root of L:
split there as IntegrateOverAPowerOfXBesideABlock(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) splits at 0. With
s = x - r, r = -g/h, N/B has a power series in s, and its first
k terms P are the part over s^k: N/(s^k B) = P/s^k + R/B, with
R = (N - P B)/s^k exactly.

Remarks

1/(x (a + b (c + d x)^3)) is 1/((u - c)(a + b u^3)) in u = c + d x: a
linear beside a binomial, which nothing took apart, since the split over written
factors takes linear and quadratic blocks only. The coefficients of N and B at the
root are read by Taylor's formula, and the block is left as it is written, for the
rules that read it. Rubi's 1.3.1.
https://github.com/asc-community/AngouriMath/issues/718
Over a power of a block the root is a fresh symbol while the series and the rest are
computed, every denominator is a written power of the block's bases at it, and the rest
is summed over one of them, written in powers of the base, and integrated in named
coefficients: with the root carried as -d/e, 1/((d + e x)^2 (a + c x^4)^3) came to 203,730 characters after 27 seconds, the lowest terms giving up on coefficients
of thousands of nodes, and is 11,068 in half a second now. Rubi's 1.3.1:568 and 569.
https://github.com/asc-community/AngouriMath/issues/233

























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