清华大学微积分高等数学第4讲不定积分二省名师优质课赛课获奖课件市赛课一等奖课件.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。感谢,作 业,P137,习题5.4,1(2)(6)(10).2(4)(13).3.,P142,习题5.5,1(3)(12).2(3).3(2).7(4).(10).,复习:,P135141,预习:P143155,1/39,6/7/2025,1,第十四讲 不定积分,（二）,一、变量代换法,二、分部积分法,2/39,6/7/2025,2,经常碰到相反情况,一、变量代换法,凑微分法,难求！,轻易求！,难求！,轻易求！,3/39,6/7/2025,3,解,4/39,6/7/2025,4,定理2：（变量代换法）,证,5/39,6/7/2025,5,解,6/39,6/7/2025,6,解,7/39,6/7/2025,7,8/39,6/7/2025,8,解,9/39,6/7/2025,9,10/39,6/7/2025,10,“双曲代换”和 “倒数代换”,11/39,6/7/2025,11,12/39,6/7/2025,12,二、分部积分法,难求！,轻易求！,轻易求！,难求！,分部积分公式,13/39,6/7/2025,13,解,更难求！,轻易求！,14/39,6/7/2025,14,解,15/39,6/7/2025,15,解,16/39,6/7/2025,16,解,17/39,6/7/2025,17,解,出现方程式,回归,18/39,6/7/2025,18,回归,解法一,19/39,6/7/2025,19,解法二,20/39,6/7/2025,20,出现恒等式,问题出在此,解法三不可取！,解法三,21/39,6/7/2025,21,利用分部积分推导递推公式,解,22/39,6/7/2025,22,23/39,6/7/2025,23,24/39,6/7/2025,24,解,25/39,6/7/2025,25,得递推公式,26/39,6/7/2025,26,小结：以下积分能够用分部积分法,27/39,6/7/2025,27,解,28/39,6/7/2025,28,29/39,6/7/2025,29,解,35,30/39,6/7/2025,30,三、有理函数积分,（一）代数有理函数积分,31/39,6/7/2025,31,四类最简分式积分,32/39,6/7/2025,32,33/39,6/7/2025,33,34/39,6/7/2025,34,35/39,6/7/2025,35,练习,36/39,6/7/2025,36,以下题目不用计算马上写出结果,37/39,6/7/2025,37,38/39,6/7/2025,38,39/39,6/7/2025,39,