Science and Education Publishing International Transaction of Electrical and Computer Engineers System 2373-1281 4 1 2017 3 6 Methods for Evaluating Some Integrations Involving Inverse Trigonometric Functions 8 13 EN Chii-Huei Yu Department of Information Technology, Nan Jeon University of Science and Technology, Tainan City, Taiwan ITECES2017412 10.12691/iteces-4-1-2 2016 9 15 2016 12 23 2017 3 4 This paper uses the mathematical software Maple as the auxiliary tool to study the integral problems. The infinite series expressions of some types of indefinite integrals involving the powers of inverse trigonometric functions can be obtained by using power series expansions, binomial series and integration term by term theorem. Moreover, some examples are proposed to demonstrate the calculations. The research approach adopted in this study is to get the answers through manual calculations and then use Maple to verify the answers. This kind of research method not only allows us to find the calculation errors, but also helps us to modify the direction of original thinking from manual calculation and Maple calculation. Therefore, Maple provides us insights into the problems.