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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)axb|14 2dxab223(48)15axbaxbC15 xln(0)2arctxbb16 2dxa dxax17 bxbb18 2da d2axxa(三)含有 的积
2、分x19 =2a1rctnxCa20 =2d()nx2212213d()()()n nxa 21 =2xa1laCx(四)含有 的积分(0)b22 2dxa1arctn(0)lxbbC23 2xb21lnab24 2da2dx|25 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 2
3、3d()x21xa35 2xa222ln()xaC|36 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()x21x|49 2dxa222lnaxxaC50 23()x 22lxa51 2da1rcosC52 22x2x53 da222lnaxaC54 23
4、()x22423(5)ln88xxa55 da31a56 22xx4222()ln88axxaC57 2da2arcosC58 2x22lnxx(八)含有 的积分2a(0)59 2dxrcsinxC60 23()ax22ax61 2dC|62 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 2dx
5、ac 21lnxbaxbcC74 b24a|2234ln8acbxaxbcC75 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 i|85 tandxlcosxC86 coi87 sedxlnta()42xlnsectaxC88 cltCl
6、ot89 2sedxtan90 cco91 setaxsexC92 cdc93 2sinx1sin24x94 coC95 sidnx121sicosindnxx96 cc97 sinx12sinsinxx98 dcodcoco99 simn1 21sicosindmnmx 2x100 sincodaxb11cos()cos()2()2()ababxC101 i in()in()()()x|102 cosdaxb11sin()sin()2()2()abxabxC103 sinabx22tarcCbb2()104 dsix22tn1laxa2()b105 cosabrctn(ta)2bbxCa2(
7、)a106 dcsxt1lan2bxb2()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()arsin44xa|115 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
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