高等数学讲义之积分表公式推导

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1、《高等数学讲义——积分公式》ByDanielLau高等数学高等数学高等数学高等数学积积积积分分分分表表表表Lau公公公公式式式式推推推推导导导导Daniel《高等数学讲义——积分公式》ByDanielLauLauDaniel《高等数学讲义——积分公式》ByDanielLau目目录录（一）含有（一）（一）含有含有ax+b的积分（1~9）·······················································1（二）含有（二）（二）含有含有ax+b的积分（10~18）············

2、·······································522（三）含有（三）（三）含有含有x±a的积分（19~21）····················································92（四）含有（四）（四）含有含有ax+b(a>)0的积分（22~28）············································112（五）含有（五）（五）含有含有ax+bx+c(a>)0的积分（29~30）·······················

3、·················1422（六）含有（六）（六）含有含有x+a(a>)0的积分（31~44）·········································1522（七）含有（七）（七）含有含有x−a(a>)0的积分（45~58）·········································2422（八）含有（八）（八）含有含有a−x(a>)0的积分（59~72）·········································Lau372（九）含有（九）

4、（九）含有含有±a+bx+c(a>)0的积分（73~78）····································48x−a（十）含有（十）（十）含有含有±或(x−a)(b−x)的积分（79~82）···························51x−b（十一）含有三角函数的积分（十一）含有三（十一）含有三角函数的积分角函数的积分（83~112）···········································55（十二）含有反三角函数的积分（其中（十二）含有反（十二）含有反三角函

5、数的积分（其中三角函数的积分（其中a>0)（113~121）·······················68（十三）含有指数函数的积分（十三）含有指（十三）含有指数函数的积分数函数的积分Daniel（122~131）··········································73（十四）含有对数函数的积分（十四）含有对（十四）含有对数函数的积分数函数的积分（132~136）··········································78（十五）含有双曲函数的积分（十五）含有双

6、（十五）含有双曲函数的积分曲函数的积分（137~141）··········································80（十六）定积分（（十六）定积分十六）定积分（142~147）····························································81附录：常数和基本初等函数导数公式附录：常数和基附录：常数和基本初等函数导数公式本初等函数导数公式·········································85说明········

7、·············································································86团队人员团队人团队人员员··············································································87《高等数学讲义——积分公式》ByDanielLauLauDaniel《高等数学讲义——积分公式》ByDanielLau（一）含有（一）含有（一）含有ax+b的积分（1~9）dx11.∫=⋅

8、lnax+b+Cax+ba1b证明：被积函数f()x=的定义域为{x

9、x≠−}ax+ba1令ax+b=t(t≠)0，则dt=adx,∴dx=dtadx11∴∫=∫dtax+bat1=⋅lnt+Cadx1将t=ax+b代入上式得：∫=⋅lnax+b+Cax+baμ1μ+12.∫(ax+b)d