Integration of Rational Functions

Abstract

A rational function can always be integrated, that is, the integral of such a function is always an elementary function. The integration procedure is complex and consists of four steps: elimination of the common zero-points of the numerator and denominator, reduction to a true rational function, decomposition into partial fractions and integration of the obtained expressions using direct integration, substitution method or partial integration method. Integrating rational functions is important because integrals of rational functions of trigonometric functions as well as integrals of some irrational functions are reduced to integrals of rational functions by appropriate transformations.