1常用积分公式(一)含有axb的积分(0a)1.dxaxb=1lnaxbCa2.()daxbx=11()(1)axbCa(1)3.dxxaxb=21(ln)axbbaxbCa4.2dxxaxb=22311()2()ln2axbbaxbbaxbCa5.d()xxaxb=1lnaxbCbx6.2d()xxaxb=21lnaaxbCbxbx7.2d()xxaxb=21(ln)baxbCaaxb8.22d()xxaxb=231(2ln)baxbbaxbCaaxb9.2d()xxaxb=211ln()axbCbaxbbx(二)含有axb的积分10.daxbx=32()3axbCa11.dxaxbx=322(32)()15axbaxbCa12.2dxaxbx=222332(15128)()105axabxbaxbCa13.dxxaxb=22(2)3axbaxbCa14.2dxxaxb=22232(348)15axabxbaxbCa215.dxxaxb=1ln(0)2arctan(0)axbbCbbaxbbaxbCbbb16.2dxxaxb=d2axbaxbxbxaxb17.daxbxx=d2xaxbbxaxb18.2daxbxx=d2axbaxxxaxb(三)含有22xa的积分19.22dxxa=1arctanxCaa20.22d()nxxa=2221222123d2(1)()2(1)()nnxnxnaxanaxa21.22dxxa=1ln2xaCaxa(四)含有2(0)axba的积分22.2dxaxb=1arctan(0)1ln(0)2axCbbabaxbCbabaxb23.2dxxaxb=21ln2axbCa24.22dxxaxb=2dxbxaaaxb25.2d()xxaxb=221ln2xCbaxb26.22d()xxaxb=21daxbxbaxb327.32d()xxaxb=22221ln22axbaCbxbx28.22d()xaxb=221d2()2xxbaxbbaxb(五)含有2axbxc(0)a的积分29.2dxaxbxc=222222222arctan(4)44124ln(4)424axbCbacacbacbaxbbacCbacbacaxbbac30.2dxxaxbxc=221dln22bxaxbxcaaaxbxc(六)含有22xa(0)a的积分31.22dxxa=1arshxCa=22ln()xxaC32.223d()xxa=222xCaxa33.22dxxxa=22xaC34.223d()xxxa=221Cxa35.222dxxxa=22222ln()22xaxaxxaC36.2223d()xxxa=2222ln()xxxaCxa37.22dxxxa=221lnxaaCax38.222dxxxa=222xaCax39.22dxax=22222ln()22xaxaxxaC440.223()dxax=22224223(25)ln()88xxaxaaxxaC41.22dxxax=2231()3xaC42.222dxxax=4222222(2)ln()88xaxaxaxxaC43.22dxaxx=2222lnxaaxaaCx44.222dxaxx=2222ln()xaxxaCx(七)含有22xa(0)a的积分45.22dxxa=1archxxCxa=22lnxxaC46.223d()xxa=222xCaxa47.22dxxxa=22xaC48.223d()xxxa=221Cxa49.222dxxxa=22222ln22xaxaxxaC50.2223d()xxxa=2222lnxxxaCxa51.22dxxxa=1arccosaCax52.222dxxxa=222xaCax53.22dxax=22222ln22xaxaxxaC54.223()dxax=22224223(25)ln88xxaxaaxxaC55.22dxxax=2231()3xaC556.222dxxax=4222222(2)ln88xaxaxaxxaC57.22dxaxx=22arccosaxaaCx58.222dxaxx=2222lnxaxxaCx(八)含有22ax(0)a的积分59.22dxax=arcsinxCa60.223d()xax=222xCaax61.22dxxax=22axC62.223d()xxax=221Cax63.222dxxax=222arcsin22xaxaxCa64.2223d()xxax=22arcsinxxCaax65.22dxxax=221lnaaxCax66.222dxxax=222axCax67.22daxx=222arcsin22xaxaxCa68.223()daxx=222243(52)arcsin88xxaxaxaCa69.22dxaxx=2231()3axC70.222dxaxx=42222(2)arcsin88xaxxaaxCa671.22daxxx=2222lnaaxaxaCx72.222daxxx=22arcsinaxxCxa(九)含有2axbxc(0)a的积分73.2dxaxbxc=21ln22axbaaxbxcCa74.2daxbxcx=224axbaxbxca2234ln228acbaxbaaxbxcCa75.2dxxaxbxc=21axbxca23ln222baxbaaxbxcCa76.2dxcbxax=212arcsin4axbCabac77.2dcbxaxx=2232242arcsin484axbbacaxbcbxaxCaabac78.2dxxcbxax=23212arcsin24baxbcbxaxCaabac(十)含有xaxb或()()xabx的积分79.dxaxxb=()()ln()xaxbbaxaxbCxb80.dxaxbx=()()arcsinxaxaxbbaCbxbx81.d()()xxabx=2arcsinxaCbx()ab82.()()dxabxx=22()()()arcsin44xabbaxaxabxCbx7()ab(十一)含有三角函数的积分83.sindxx=cosxC84.cosdxx=sinxC85.tandxx=lncosxC86.cotdxx=lnsinxC87.secdxx=lntan()42xC=lnsectanxxC88.cscdxx=lntan2xC=lncsccotxxC89.2secdxx=tanxC90.2cscdxx=cotxC91.sectandxxx=secxC92.csccotdxxx=cscxC93.2sindxx=1sin224xxC94.2cosdxx=1sin224xxC95.sindnxx=1211sincossindnnnxxxxnn96.cosdnxx=1211cossincosdnnnxxxxnn97.dsinnxx=121cos2d1sin1sinnnxnxnxnx98.dcosnxx=121sin2d1cos1cosnnxnxnxnx99.cossindmnxxx=11211cossincossindmnmnmxxxxxmnmn=11211cossincossindmnmnnxxxxxmnmn100.sincosdaxbxx=11cos()cos()2()2()abxabxCabab8101.sinsindaxbxx=11sin()sin()2()2()abxabxCabab102.coscosdaxbxx=11sin()sin()2()2()abxabxCabab103.dsinxabx=2222tan22arctanxabCabab22()ab104.dsinxabx=222222tan12lntan2xabbaCxbaabba22()ab105.dcosxabx=2arctan(tan)2ababxCababab22()ab106.dcosxabx=tan12lntan2xababbaCabbaxabba22()ab107.2222dcossinxaxbx=1arctan(tan)bxCaba108.2222dcossinxaxbx=1tanln2tanbxaCabbxa109.sindxaxx=211sincosaxxaxCaa110.2sindxaxx=223122cossincosxaxxaxaxCaaa111.cosdxaxx=211cossinaxxaxCaa112.2cosdxaxx=223122sincossinxaxxaxaxCaaa(十二)含有反三角函数的积分(其中0a)113.arcsindxxa=22arcsinxxaxCa114.arcsindxxxa=2222()arcsin244xaxxaxCa115.2arcsindxxxa=322221arcsin(2)39xxxaaxCa116.arccosdxxa=22arccosxxaxCa9117.arccosdxxxa=2222()arccos244xaxxaxCa118.2arccosdxxxa=322221arccos(2)39xxxaaxCa119.arctandxxa=22arctanln()2xaxaxCa120.arctandxxxa=221()arctan22xaaxxCa121.2arctandxxxa=33222arctanln()366xxaaxaxCa(十三)含有指数函数的积分122.dxax=1lnxaCa123.edaxx=1eaxCa124.edaxxx=21(1)eaxaxCa125.ednaxxx=11eednaxnaxnxxxaa126.dxxax=21ln(ln)xxxaaCaa127.dnxxax=11dlnlnnxnxnxaxaxaa128.esindaxbxx=221e(sincos)axabxbbxCab129.ecosdaxbxx=221e(sincos)axbbxabxCab130.esindaxnbxx=12221esin(sincos)