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IntegrateAPolynomialOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable)

Method (no overloads)

Summary

A polynomial over a power of a linear, P(x)/(a + b x)^k with k >= 2,
under t = a + b x: P((t - a)/b) t^(-k) / b is a sum of powers of
t, each a power rule or a logarithm.

Remarks

(c + d x)/(3 + 5 x)^2 came out and (c + d x)/(a + b x)^2 did not: the
first has a rational root to split at, the second has none, and no other rule read
the shape. 1/(a + b x)^2 was answered by the quadratic rule, as a piecewise on
a discriminant that is identically zero. This is what the symbolic partial-fraction
split hands on for a repeated linear factor, and it was declined there for want of
this.
After the splits over the rationals, so that a numeric coefficient keeps the answer
it had. b is divided by, in the generic case as everywhere here; a decidably
zero b is not a linear at all and is declined.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

Table of contents

AngouriMath

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

IntegrateAPolynomialOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable)