Integration by partial fractions evaluates a rational function integral by decomposing the integrand
into simpler fractions. After polynomial division
when necessary, a proper rational function , for which
, is written as a sum of terms associated
with the linear factors and quadratic irreducible polynomials that occur as factors
of
. For example,
This formula holds for .
The resulting terms integrate to combinations of logarithms,
rational functions, and inverse
tangent functions.