不定积分∫eaxsin（βx）dx计算方法的探究  

Investigation on ways to compute the integral ∫eaxsin（βx）dx

作　　者：王成强 WANG Cheng-qiang(School of Mathematics,Chengdu Normal University,Chengdu 611130,China)

机构地区：[1]成都师范学院数学学院

出　　处：《高师理科学刊》2019年第10期59-62,共4页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(11701050,11571244);四川省教育厅项目(18ZB0098);成都师范学院校级培育项目(CS18ZD07);成都师范学院校级教改项目(2017JG13)

摘　　要：基于分部积分法、换元积分法、待定系数法和代数法等方法,给出典型不定积分∫e^αxsin(βx)dx的10种解答方法,这些研究结果将常用的依附于不同问题的不定积分方法通过一道具体问题联系起来,启示尝试利用多种视角发现不定积分问题的解题思路,帮助加深对不定积分理论的理解.Based on the methods of integral by parts,integration by the change of variables,undetermined coefficient and algebra,etc,10 methods are provided to compute a typical indefinite integral ∫e^αxsin(βx)dx.These results link the commonly used indefinite integral methods attached to different problems with a specific problem,encourage to attempt to use a variety of perspectives to discover the problem-solving ideas of the concerned indefinite integral problem,and thus help to understand better the indefinite integral theory.

关 键 词：大学数学 不定积分 分部积分法 换元积分法 

分 类 号：O172.2[理学—数学] G642.0[理学—基础数学]