A Study on the Integrals of Rational Functions with Maple

Abstract

This article uses the mathematical software Maple as an auxiliary tool to study the integral problems of  rational functions. We can use binomial series and  integration term by term theorem to find the infinite series form of the indefinite integral of some type of rational function, and hence greatly reducing the difficulty of evaluateits definite integral. On the other hand, we propose two rational functions to find their definite integrals, and the answers of these definite integrals are presented in infinite series forms. The research method adopted in this paper is to find out the answers, and then uses Maple to verify our results. This kind of research method not only allows us to find the calculation errors, but also can help us to amend the original thinking direction  because we can verify the correctness of our theory from the consistency of manual and Maple calculations. Therefore, Maple can give us the inspiration of the problem and let us find theanswersof the problems.