1、常 用 积 分 公 式（一）含有 的积分( )axb0a1 d1lnC2 （ ）()x1()xba13 dab21lna4 2x223()()lnxbxbaxbC 5 d()xab1lnaC6 2()2lxb7 2d()xab21(ln)aCx8 2()x23(l)bba9 2d()ab21ln()xCx（二）含有 的积分10 dx3()axb11 ab32()15axbC12 2x2233(18()0axb13 dab2)axb14 2dxab223(48)15axbaxbC15 xln(0)2arctxbb16 2dxa dxax17 bxbb18 2da d2axxa（三）含有 的积分x
2、19 =2a1rctnxCa20 =2d()nx2212213d()()()n nxa 21 =2xa1laCx（四）含有 的积分(0)b22 2dxa1arctn(0)lxbbC23 2xb21lnab24 2da2dx25 2d()xab21lnxCab26 2()x2dx27 32d()ab2221lnabCx28 2()x22d()x（五）含有 的积分abc0a29 2dxabc222222rctan(4)441lxbCbacbacx 30 2dxc 2dlnbxacc（六）含有 的积分2(0)31 2xa1rshxC2ln()xaC32 23d()x22xa33 2aC34 23d(
3、)x21xa35 2xa222ln()xaC36 23d()xa 22ln()xxaCa37 2x1lnx38 22da2aC39 x222ln()xxaC40 23()da22423(5)ln()88axa41 x31xC42 22da4222()ln()88axaC43 2x22lnxax44 2dax22l()aCx（七）含有 的积分2(0)45 =2dxa1rchxCa2lnxa46 23()x22x47 2daaC48 23()x21x49 2dxa222lnaxxaC50 23()x 22lxa51 2da1rcosC52 22x2x53 da222lnaxaC54 23()x22
4、423(5)ln88xxa55 da31a56 22xx4222()ln88axxaC57 2da2arcosC58 2x22lnxx（八）含有 的积分2a(0)59 2dxrcsinxC60 23()ax22ax61 2dC62 23d()xa21Cax63 2x22arcsinx64 23d()ax2riCax65 221ln66 22dxa2axC67 22arcsinx68 23()dax2243(5)arcsin88xC69 31axC70 22dxax422()arcsin88x71 2 22lnaCx72 2dax2rcsix（九）含有 的积分2b(0)a73 2dxac 21l
5、nxbaxbcC74 b24a2234ln8acbxaxbcC75 2dxabc2123lnbaxaxbcC76 2dxcba 21rcsi4bCc77 232arcsin484x xbaxCac78 2dxcba 2321ribc（十）含有 或 的积分x()bx79 dab()()ln)aaxbC80 x()()rcsixb81 d()xab2arcsinCx()ab82 x 2()arcsin44bxxCb()（十一）含有三角函数的积分83 sindxcosxC84 i85 tandxlcosxC86 coi87 sedxlnta()42xlnsectaxC88 cltClot89 2se
6、dxtan90 cco91 setaxsexC92 cdc93 2sinx1sin24x94 coC95 sidnx121sicosindnxx96 cc97 sinx12sinsinxx98 dcodcoco99 simn1 21sicosindmnmx 2x100 sincodaxb11cos()cos()2()2()ababxC101 i in()in()()()x102 cosdaxb11sin()sin()2()2()abxabxC103 sinabx22tarcCbb2()104 dsix22tn1laxa2()b105 cosabrctn(ta)2bbxCa2()a106 dcs
7、xt1lan2bxb2()b107 22osinaxrct()C108 22dcib1anltbx109 sinxa2sncosx110 2d231incosaxaC111 cosx2csx112 2a23incsixa（十二）含有反三角函数的积分（其中 ）0113 rcsindx2rcsixC114 ai22()arsin44xa115 2arcsindx3221arcsin()9xaxC116 o2o117 arcsdx22()arcs44xax118 2ro3221ro()9C119 actndx 2actnlxax120 r21()rt121 2actndx3322actnln()6xaxC（十三）含有指数函数的积分122 x1lxC123 edaa124 x2(1)eax125 ena1dnnx126 dx2l(l)xxaC127 nxa11dllnxx128 esidb2e(sicos)ab129 coax xxC130 esin 12esin(sics)anbxb
