高等数学讲义之积分表公式推导.pdf

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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公公公公式式式式推推推推导导导导《高等数学讲义——积分公式》ByDanielLau《高等数学讲义——积分公式》ByDanielLau目目录录（一）含有（一）含有ax+b的积分（1~9）·······················································1（二）含有（二）含有ax+b的积分（10~18）···································

2、················522（三）含有（三）含有x±a的积分（19~21）····················································92（四）含有（四）含有（四）含有ax+b(a>)0的积分（22~28）············································112（五）含有（五）含有（五）含有ax+bx+c(a>)0的积分（29~30）········································1422（六

3、）含有（六）含有（六）含有x+a(a>)0的积分（31~44）·········································1522（七）含有（七）含有（七）含有x−a(a>)0的积分（45~58）·········································2422（八）含有（八）含有（八）含有a−x(a>)0的积分（59~72）·········································372（九）含有（九）含有（九）含有±a+bx+c(a>)0的积

4、分（73~78）····································48x−a（十）含有（十）含有（十）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）含有三角（十一）含有三角函数的积分函数的积分（83~112）···········································55（十二）含有反三角函数的积分（其中（十二）含有反三（十二）含有反三角函数的积分（其中角函数的积分（其

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

6、积分（137~141）··········································80（十六）定积分（十六（十六）定积分）定积分（142~147）····························································81附录：常数和基本初等函数导数公式附录：常数和基本附录：常数和基本初等函数导数公式初等函数导数公式·········································85说明····················

7、·································································86团队人员团团队人员团队人员··············································································87《高等数学讲义——积分公式》ByDanielLau《高等数学讲义——积分公式》ByDanielLau（一）含有ax+b的积分（1~9）dx11.∫=⋅lnax+b+Cax+ba1b证明：被积函数f()

8、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)dx=⋅(ax+b)+C(μ≠−1)a(μ+)11证明：令ax+b=t,则dt=adx,∴dx=dtaμ1μ∴∫(ax+b