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

 Method (no overloads)

Summary

A polynomial over a power of a binomial, P(x)/(a + b x^n)^k with n >= 3 and k >= 2, a power at a time down to P'(x)/(a + b x^n), which
IntegrateAPolynomialOverABinomial(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable) answers at the roots of unity.

Remarks

For a monomial, with B = a + b x^n,
int x^m/B^j = x^(m+1)/(a n (j - 1) B^(j-1)) - (m + 1 - n (j - 1))/(a n (j - 1)) int x^m/B^(j-1)

since the derivative of x^(m+1)/B^(j-1) is (m + 1) x^m/B^(j-1) - (j - 1) n b x^(m+n)/B^j and b x^(m+n) = x^m B - a x^m. Each monomial of P goes down the powers on
its own, and what reaches the first power is gathered into one polynomial over
B, integrated once.
 After the Hermite reduction, which answers the square and the cube of a binomial with
symbols in it in one linear solve and keeps those answers. Its system grows with
n k: 1/(a + b x^4)^3 is answered and 1/(a + b x^4)^4 was declined.
The constant term is divided by, which is the generic case, as everywhere in the
integrator.
https://github.com/asc-community/AngouriMath/issues/718

























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