《高等数学《概率论与数理统计》常用积分表》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（12页珍藏版）》请在金锄头文库上搜索。
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+
2、的积分的积分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+222222222ar
3、ctan(4)44124ln(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+ 3822
4、2dxxxa+222xaCa x+ 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+
5、 4448223d()xxxa221Cxa+ 49222dxxxa22222ln22xaxaxxa+C 50222 3d()xxxa2222lnxxxaCxa+ 5122dxxxa1arccosaCax+ 52222dxxxa222xaCa x+ 5322dxax22222ln22xaxaxxa+C 54223() dxax22224223(25)ln88xxaxaaxxaC+ 5522dx xax2231()3xaC+ 56222dxxax4222222(2)ln88xaxaxaxxaC+ 5722dxaxx22arccosaxaaCx+ 58222dxaxx2222lnxaxxaCx+ （
6、八）含有（八）含有22ax(0a )的积分的积分 5922dxaxarcsinxCa+ 6022d()xax3222xCaax+ 556122dxxax22axC+ 62223d()xxax221Cax+ 63222dxxax222arcsin22xaxaxCa+ 64222 3d()xxax22arcsinxxCaax+ 6522dxx ax221lnaaxCax+ 66222dxxax222axCa x+ 66722daxx222arcsin22xaaxCa+x 68223()axdx222243(52)arcsin88xxaxaxaaC+ 6922dx axx2231()3axC+ 70
7、222dxaxx42222(2)arcsin88xaxxaaxCa+ 7122daxxx2222lnaaxaxaCx+ 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+223224arcsin484
8、axbbacaxbcbxaxCaabac+2 782dxxcbxax+23212arcsin24baxbcbxaxCaabac+ （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 106dcos
9、xabx+tan12lntan2xababbaCabbaxabba+22()ab113arcsin dxxa22arcsinxxaxCa+ 9114arcsindxxxa2222()arcsin244xaxxaxCa+ 1152arcsin dxxxa322221arcsin(2)39xxxaaxCa+ 116arccos dxxa22arccosxxaxCa+ 117arccos dxxxa2222()arccos244xaxxaxCa+ 1182arccosdxxxa322221arccos(2)39xxxaaxCa+ 119arctandxxa22arctanln()2xaxaxCa+
10、120arctandxxxa221()arctan22xaaxxCa+ 1212arctandxxxa33222arctanln()366xxaaxaxCa+ （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 co
11、sdaxbx x221e ( sincos)axbbxabxCab+ 1010130e sindaxnbx x12221e sin( sincos)axnbx 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+
12、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
