基于结构特征的三角函数有理式不定积分的解析与探究  

Analysis and Exploration of the Indefinite Integral of Rational Trigonometric Function Based on Structural Feature

作　　者：贾瑞玲 孙铭娟 文生兰[1] 

机构地区：[1]信息工程大学,河南 郑州

出　　处：《应用数学进展》2023年第9期4049-4056,共8页Advances in Applied Mathematics

摘　　要：三角函数有理式不定积分是积分学的一个重要组成部分,是解决三角函数问题的关键。由于其计算方法灵活多变且技巧性强,这给很多学生带来了困难。许多学者对这方面也进行了探索和研讨。在前人研究的基础上,本文深入阐述了具有结构特征的三角函数有理式的不定积分,突出分析和科学抽象的全过程,潜移默化地培养学生探索问题、剖析细节、提炼精髓、升华思维的能力。The indefinite integral of rational trigonometric function is an important part of integral theory and the key to solving trigonometric function problem. Because of its flexible calculation methods and strong skills, it brings difficulties to many students. Many scholars have also explored and discussed this aspect. Based on previous studies, this paper deeply expounds the indefinite integral of ration-al trigonometric function with structural feature, highlights the whole process of analysis and scien-tific abstraction, and subtly cultivates students’ ability to explore problems, analyze details, refine essence and sublimate thinking.

关 键 词：结构特征 三角函数有理式 不定积分 变量代换 联合积分法 

分 类 号：O17[理学—数学]