Integrals of Rational Functions

C.    INTEGRALS OF RATIONAL FUNCTIONS

In Section 8.8 we explained how to integrate any rational function. The only part of the procedure which requires guesswork is factoring the denominator into linear and quadratic terms. Once that is done, any rational function can be integrated in a routine manner.

The integrals in lists A and B (which can be found in tables) and the rational integrals are easily recognized. Now we come to grips with the real problem. Given an integral which cannot be found in a table, we wish to transform it into either a rational integral or an integral which can be found in a table. We have three main methods for transforming integrals: using the Sum Rule, integration by change of variables, and integration by parts.