关于一类三角函数有理式积分问题的研究  

A Study on Integral of a Class of Rational Trigonometric Function

作　　者：魏晋桃 王杉林 WEI Jintao;WANG Shanlin(School of Mechatronics and Information Engineering,Chongqing College of Humanities,Science&Technology,Chongqing Hechuan 401524;Mathematics Teaching Department,Lanzhou Technology and Business College,Lanzhou 730101)

机构地区：[1]重庆人文科技学院机电与信息工程学院,重庆合川401524 [2]兰州工商学院大学数学部,甘肃兰州730101

出　　处：《高等数学研究》2024年第6期15-16,75,共3页Studies in College Mathematics

摘　　要：本文研究了积分∫_(0)^(2π)1/a+bcosx dx(a≠0,b≠0)的计算问题.首先分析此类积分求解中常见的问题;其次分情况讨论此类积分的敛散性,并在收敛时推导出计算公式.This paper focuses on the integral∫_(0)^(2π)1/a+bcosx dx(a≠0,b≠0),beginning with an analysis of common problems in solving such integrals.It then discusses convergence and divergence in various scenarios and derives the calculation formula for convergent integrals.

关 键 词：三角函数有理式 定积分 反常积分 敛散性 

分 类 号：O172.2[理学—数学]