Some Improper Integral Problems

Abstract

This paper takes advantage of the mathematical software Maple to study two types of improper integrals. The infinite series formsof these two types of improper integrals can be obtained by using differentiation with respect to a parameter and differentiation term by term theorem.In addition, two examples of improper integrals are proposed and we actually find their infinite series forms. The research method adopted in this article is to obtain the answers by manual calculation, and then uses Maple to verify the answers. This research method not only allows us to find the calculation errors, but also helps us to amend the original thinking direction  because we can verify the correctness of our theory from the consistency of manual and Maple calculations.