清华微积分(高等数学)课件第十五讲不定积分.ppt

2023/6/30,1,作业P150 习题5.6 1(5)(7)(15).2(3).3(1).4(5).5(1)(3).P155 综合题 23.24.30.48.63.,复习：P124155 预习：P158166,2023/6/30,2,第十五讲 不定积分（三）,一、有理函数的积分,二、简单无理式的积分,2023/6/30,3,一、有理函数的积分,（一）代数有理函数的积分,2023/6/30,4,四类最简分式的积分,2023/6/30,5,2023/6/30,6,2023/6/30,7,如何将真分式分解为最简分式之和？,定理1：,2023/6/30,8,定理2：,2023/6/30,9,2023/6/30,10,解,2023/6/30,11,2023/6/30,12,解,2023/6/30,13,2023/6/30,14,2023/6/30,15,注意 计算最后一个积分时,利用了递推公式,2023/6/30,16,遇到有理函数的积分要灵活处理,2023/6/30,17,有理函数,万能代换,（二）三角有理函数的积分,代数有理函数的积分,2023/6/30,18,解,2023/6/30,19,三角函数有理式积分的最常用的方法是用三角恒等式将问题化简,2023/6/30,20,2023/6/30,21,解,2023/6/30,22,解一,2023/6/30,23,解二,2023/6/30,24,二、简单无理式的积分,代数有理函数的积分,2023/6/30,25,代数有理函数的积分,2023/6/30,26,代数有理函数的积分,2023/6/30,27,2023/6/30,28,解,2023/6/30,29,解,2023/6/30,30,2023/6/30,31,解,2023/6/30,32,三角形法,2023/6/30,33,2023/6/30,34,练习,2023/6/30,35,以下题目不用笔算立即写出结果,2023/6/30,36,2023/6/30,37,