高等数学《概率论与数理统计》常用积分表.pdf

《高等数学《概率论与数理统计》常用积分表.pdf》由会员分享，可在线阅读，更多相关《高等数学《概率论与数理统计》常用积分表.pdf（12页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、常常 用用 积积 分分 公公 式式（一）含有的积分（一）含有的积分()axb+0a 1dxaxb+1ln axbCa+2()axbx+d11()(1)axbCa+（1）3dxxaxb+21(ln)axbbaxbCa+42dxxaxb+22311()2()ln2axbb axbbaxbCa+5d()xx axb+1lnaxbCbx+62d()xxaxb+21lnaaxbCbxbx+72d()xxaxb+21(ln)baxbCaax+b822d()xxaxb+231(2 ln)baxbbaxbCaaxb+92d()xx axb+211ln()axbCb axbbx+（二）含有（二）含有axb+的积

2、分的积分10daxb x+32()3axbCa+11dx axb x+322(32)()15axbaxbCa+122dxaxb x+222332(15128)()105a xabxbaxbCa+13dxxaxb+22(2)3axbaxbCa+1概率论与数理统计-常用积分表(直接打印)1142dxxaxb+22232(348)15a xabxbaxbCa+15dxx axb+1ln(0)2arctan(0)axbbCbbaxbbaxbCbbb+)222dxaxb+1arctan(0)1ln(0)2axCbbabaxbCbabaxb+)292dxaxbxc+222222222arctan(4)44

3、124ln(4)424axbCbacbacbaxbbacCbacbacaxbbac+ac 302dxxaxbxc+221dln22bxaxbxcaaaxbxc+（六）含有（六）含有22xa+(0a )的积分的积分 3122dxxa+1arshxCa+22ln()xxaC+32223d()xxa+222xCaxa+3322dxxxa+22xaC+34223d()xxxa+221Cxa+3335222dxxxa+22222ln()22xaxaxxa+C 36222 3d()xxxa+2222ln()xxxaCxa+3722dxxxa+221lnxaaCax+38222dxxxa+222xaCa x

4、+3922dxax+22222ln()22xaxaxxa+C 40223()dxax+22224223(25)ln()88xxaxaaxxaC+4122dx xa+x2231()3xaC+42222dxxa+x4222222(2)ln()88xaxaxaxxaC+4322dxaxx+2222lnxaaxaaCx+44222dxaxx+2222ln()xaxxaCx+（七）含有（七）含有22xa(0a )的积分的积分 4522dxxa1archxxCxa+=22ln xxaC+4622d()x3xa222xCaxa+4722dxxxa22xaC+4448223d()xxxa221Cxa+4922

5、2dxxxa22222ln22xaxaxxa+C 50222 3d()xxxa2222lnxxxaCxa+5122dxxxa1arccosaCax+52222dxxxa222xaCa x+5322dxax22222ln22xaxaxxa+C 54223()dxax22224223(25)ln88xxaxaaxxaC+5522dx xax2231()3xaC+56222dxxax4222222(2)ln88xaxaxaxxaC+5722dxaxx22arccosaxaaCx+58222dxaxx2222lnxaxxaCx+（八）含有（八）含有22ax(0a )的积分的积分 5922dxaxarc

6、sinxCa+6022d()xax3222xCaax+556122dxxax22axC+62223d()xxax221Cax+63222dxxax222arcsin22xaxaxCa+64222 3d()xxax22arcsinxxCaax+6522dxx ax221lnaaxCax+66222dxxax222axCa x+66722daxx222arcsin22xaaxCa+x 68223()axdx222243(52)arcsin88xxaxaxaaC+6922dx axx2231()3axC+70222dxaxx42222(2)arcsin88xaxxaaxCa+7122daxxx222

7、2lnaaxaxaCx+72222daxxx22arcsinaxxCxa+（九）含有（九）含有2axbxc+(0a )的积分的积分 732dxaxbxc+21ln 22axbaaxbxcCa+6742daxbxc x+224axbaxbxca+2234ln 228acbaxbaaxbxcCa+752dxxaxbxc+21axbxca+23ln 222baxbaaxbxcCa+762dxcbxax+212arcsin4axbCabac+772dcbxaxx+223224arcsin484axbbacaxbcbxaxCaabac+2 782dxxcbxax+23212arcsin24baxbcbx

8、axCaabac+（十）含有（十）含有xaxb或或()()xa bx的积分的积分 79dxaxxb()()ln()xaxbbaxaxbxbC+80dxaxbx()()arcsinxaxaxbbabxbxC+81d()(x)xa bx2arcsinxaCbx+()ab 82()()dxa bxx22()()()arcsin44xabbaxaxa bxCbx+()ab 104dsinxabx+222222tan12lntan2xabbaCxbaabba+22()ab 106dcosxabx+tan12lntan2xababbaCabbaxabba+22()ab113arcsin dxxa22arc

9、sinxxaxCa+9114arcsindxxxa2222()arcsin244xaxxaxCa+1152arcsin dxxxa322221arcsin(2)39xxxaaxCa+116arccos dxxa22arccosxxaxCa+117arccos dxxxa2222()arccos244xaxxaxCa+1182arccosdxxxa322221arccos(2)39xxxaaxCa+119arctandxxa22arctanln()2xaxaxCa+120arctandxxxa221()arctan22xaaxxCa+1212arctandxxxa33222arctanln()3

10、66xxaaxaxCa+（十三）含有指数函数的积分（十三）含有指数函数的积分 122dxax1lnxaCa+123e daxx1eaxCa+124e daxxx21(1)eaxaxCa+125e dnaxxx11eenaxnaxndxxxaa 126dxxax21ln(ln)xxxaaaaC+127dnxx ax11dlnlnnxnxnx axaaax 128e sindaxbx x221e(sincos)axabxbbxCab+129e cosdaxbx x221e(sincos)axbbxabxCab+1010130e sindaxnbx x12221e sin(sincos)axnbx

11、abxnbbxab n+22222(1)e sindaxnn nbbx xab n+131e cosdaxnbx x12221ecos(cossin)axnbx abxnbbxab n+22222(1)e cosdaxnn nbbx xab n+（十四）含有对数函数的积分（十四）含有对数函数的积分 132ln dx xlnxxxC+133dlnxxxln lnxC+134ln dnxx x111(ln)11nxxCnn+135(ln)dnxx1(ln)(ln)dnnxxnxx 136(ln)dmnxxx111(ln)(ln)d11mnmnnxxxxmm+x（十五）含有双曲函数的积分（十五）含有

12、双曲函数的积分 137sh dx xchxC+138ch dx xshxC+139th dx xlnchxC+1402shdx x1sh224xxC+1412chdx x1sh224xxC+（十六）定积分（十六）定积分 1420 cosdnx xsindnx x1430 cossindmxnx x144 coscosdmxnx x0,mnmn=1111145 sinsindmxnx x0,mnmn=1460sinsindmxnx x0coscosdmxnx x0,2mnmn=147 nI20sindnx x20cosdnx x nI21nnIn 134 225nnnInn=?3 （为大于 1 的正奇数），n1I1 133 124 2 2nnnInn=?n（为正偶数），0I2 1212