AngouriMath
SolveByPartialFractions(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A quotient of polynomials whose denominator has a rational root, split at that
root and integrated in two parts.
root and integrated in two parts.
Remarks
The rules for a linear or a quadratic denominator answer those in one piece, so
what is left over are the denominators of degree three and up, which nothing
read at all: 1/(x^3 + 1) had no antiderivative. Splitting at the root -1 leaves
(1/3)/(x + 1) and (2 - x)/(3(x^2 - x + 1)), and both of those are already
integrable, the second by the rule for a linear numerator over a quadratic.
Each step takes a degree off the denominator, so this ends.
what is left over are the denominators of degree three and up, which nothing
read at all: 1/(x^3 + 1) had no antiderivative. Splitting at the root -1 leaves
(1/3)/(x + 1) and (2 - x)/(3(x^2 - x + 1)), and both of those are already
integrable, the second by the rule for a linear numerator over a quadratic.
Each step takes a degree off the denominator, so this ends.
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