分部积分法的解题技巧  

The skills of calculating integration by parts

作　　者：张磊 王利岩 吴玉斌 王辉 ZHANG Lei;WANG Liyan;WU Yubin;WANG Hui(School of Science,Shenyang Aerospace University,Shenyang 110136,China)

机构地区：[1]沈阳航空航天大学理学院,辽宁沈阳110136

出　　处：《高师理科学刊》2022年第2期88-91,共4页Journal of Science of Teachers＇College and University

基　　金：辽宁省教育厅青年项目(L201730);辽宁省科技厅博士启动项目(201601173);沈阳航空航天大学教改项目(JG2020081)。

摘　　要：分部积分公式的作用是将积分问题化繁为简,从而达到计算目的.通过算例依次探讨了分部积分法的降幂、消去和循环作用,对照这些作用将分部积分问题分为3大类,梳理出分部积分法的使用规则.为了提高分部积分法的运算效率,对分部积分公式做了推广,借助图表生动形象地展示了求原函数的过程.通过例题分析表格法的有效性,进一步加深了学生对概念和公式的理解,提高了计算效率.The function of formulas of integration by parts is to simplify the integration problem,so as to achieve the purpose of calculation.The effects of power reduction,elimination and circulation of integration by parts are discussed by examples,according to these functions,the issues on integration by parts are divided into three categories and the rules of integration by parts are sorted out.In order to improve the efficiency of integration by parts,the formula of integration by parts was extend,and the process of finding the original function was vividly shown with the help of tables.The effectiveness of the table method is analyzed through examples to deepen students'understanding of concepts and formulas and improve calculation efficiency.

关 键 词：分部积分法 不定积分 图表法 

分 类 号：O172[理学—数学] G642.0[理学—基础数学]