Using maple to study the integrals of trigonometric functions

This paper uses Maple for the auxiliary tool to evaluate the integrals of two types of trigonometric functions. We can obtain the Fourier series expansions of these two integrals by using integration term by term. Our research way is to count the answers by hand, and then use Maple to verify our results. This research way can not only let us find the calculation errors but also help us to revise the original thinking direction because we can verify the correctness of our theory from the consistency of hand count and Maple calculations.