eng Science and Education Publishing American Journal of Systems and Software 2014-03-02 2 1 22 26 10.12691/ajss-2-1-4 AJSS2014214 article Chii-Huei Yu chiihuei@nju.edu.tw 1 Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan This paper uses the mathematical software Maple for the auxiliary tool to study four types of integrals. We can obtain the infinite series forms of these integrals by using binomial theorem and integration term by term theorem. In addition, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. http://pubs.sciepub.com/ajss/2/1/4/ajss-2-1-4.pdf integrals infinite series forms binomial theorem integration term by term theorem Maple