积分表积分公式推导.doc

高等数学
积分表
公式推导

目 录
（一）含有 ax + b的积分（1～9)·······················································1
(二)含有 ax + b的积分（10～18）···················································5
（三)含有 x ± a
2 2
的积分
(19～21)····················································9
(四）含有 ax2 +b （a 〉 0）的积分（22~28)············································11
(五）含有 ax2 +bx +c (a 〉 0)
的积分
（29～30）········································14
（六）含有 x 2 + a 2 (a 〉 0）的积分（31～44）·········································15
(a > 0)的积分(45~58）·········································24
（八）含有 a 2 − x 2 （a 〉 0)的积分（59～72)·········································37
(七）含有 x
− a
2 2
（九)含有 ± a +bx + c （a 〉 0)的积分（73～78）····································48
2
（十）含有 ±
x − a
x − b
或
（ x − a）（b − x)的积分（79~82)···························51
（十一）含有三角函数的积分
(83~112）···········································55
(十二）含有反三角函数的积分(其中 a〉0）（113~121）·······················68
（十三）含有指数函数的积分（122~131）··········································73
（十四）含有对数函数的积分
（十五)含有双曲函数的积分
（132～136)··········································78
（137~141）··········································80
（十六）定积分
（142～147）····························································81
附录：常数和基本初等函数导数公式
·········································85
说明
·····················································································86
团队人员
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