eng
Science and Education Publishing
International Transaction of Electrical and Computer Engineers System
2373-1281
2017-03-06
4
1
8
13
10.12691/iteces-4-1-2
ITECES2017412
article
Methods for Evaluating Some Integrations Involving Inverse Trigonometric Functions
Chii-Huei Yu
chiihuei@mail.nju.edu.tw
1
Department of Information Technology, Nan Jeon University of Science and Technology, Tainan City, Taiwan
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.
http://pubs.sciepub.com/iteces/4/1/2/iteces-4-1-2.pdf
infinite series expressions
indefinite integrals
inverse trigonometric functions
power series expansions
binomial series
integration term by term theorem
Maple