單擊此處編輯母版標(biāo)題樣式,單擊此處編輯母版文本樣式,第二級(jí),第三級(jí),第四級(jí),第五級(jí),*,*,作業(yè),P150,習(xí)題,5.,6,1(5)(7)(15).2(3).3(1).,4(5).5(1)(3).,P155,綜合題,23.24.30.48.63.,復(fù)習(xí)：,P124155,預(yù)習(xí)：,P158166,12/11/2024,1,第十五講 不定積分（三）,一、有理函數(shù)的積分,二、簡(jiǎn)單無理式的積分,12/11/2024,2,一、有理函數(shù)的積分,（一）代數(shù)有理函數(shù)的積分,12/11/2024,3,四類最簡(jiǎn)分式的積分,12/11/2024,4,12/11/2024,5,12/11/2024,6,如何將真分式分解為最簡(jiǎn)分式之和？,定理,1,：,12/11/2024,7,定理,2,：,12/11/2024,8,12/11/2024,9,解,12/11/2024,10,12/11/2024,11,解,12/11/2024,12,12/11/2024,13,12/11/2024,14,注意,計(jì)算最后一個(gè)積分時(shí),利用了遞推公式,12/11/2024,15,遇到有理函數(shù)的積分要靈活處理,12/11/2024,16,有理函數(shù),萬能,代換,（二）三角有理函數(shù)的積分,代數(shù)有理函數(shù)的積分,12/11/2024,17,解,12/11/2024,18,三角函數(shù)有理式積分的最常用的方法是用,三角恒等式將問題化簡(jiǎn),12/11/2024,19,12/11/2024,20,解,12/11/2024,21,解一,12/11/2024,22,解二,12/11/2024,23,二、簡(jiǎn)單無理式的積分,代數(shù)有理函數(shù)的積分,12/11/2024,24,代數(shù)有理函數(shù)的積分,12/11/2024,25,代數(shù)有理函數(shù)的積分,12/11/2024,26,12/11/2024,27,解,12/11/2024,28,解,12/11/2024,29,12/11/2024,30,解,12/11/2024,31,三角形法,12/11/2024,32,12/11/2024,33,練習(xí),12/11/2024,34,以下題目不用筆算立即寫出結(jié)果,12/11/2024,35,12/11/2024,36,12/11/2024,37,