1、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 2x223(48)15axbC215 dxab1ln(0)2arctxbCb16 2x dxbxab17 dabxax18 2 d2bab（三）含有 的积分x
2、a19 =2d1rctnxC20 =2()nxa2212213d()()()n nxaa 21 =2dx1lCx（四）含有 的积分(0)ab22 2dx1arctn(0)lxbbC23 2xab21lnab24 2d2dx25 2()xab21lnCaxb26 2d()x2d27 32()ab2221lnaxbC328 2d()xab221d()xxabab（五）含有 的积分c029 2dxabc222222arctn(4)441lxCbacbbacx 30 2dxc 2dlnbxacc（六）含有 的积分2(0)31 2xa1rshxC2ln()xaC32 23d()x22xa33 2aC34
3、 23d()x21xa35 2xa222ln()xaC36 23d()22l()xa37 2xa1lnC38 22dx2xa39 a222ln()xaC40 23()dx22423(5)ln()88xaxa41 a31C442 22dxax4222()ln()88aaxxaC43 2 22ln44 2dxa22l()xaxaC（七）含有 的积分2(0)45 =2dxa1rchxCa2lnxa46 23()x22x47 2daaC48 23()x21x49 2dxa22lnaxaC50 23() 22lxa51 2dxa1rcosC52 22x2x53 da222lnaxaC54 23()x22
4、423(5)ln88xxa55 da31a56 22xx4222()ln88axxaC557 2dxa2arcosxCx58 2x22lnx（八）含有 的积分2a(0)59 2dxrcsinxC60 23()ax22ax61 2dC62 23()xa21ax63 2dx22arcsinxC64 23()ax2riax65 2d21lnC66 22xa2ax67 d22arcsinxC68 23()ax2243(5)arcsin88x69 d31ax70 22xax422()arcsin88xC71 2d 22lnax672 2dax2arcsinxC（九）含有 的积分2b(0)73 2dxac
5、 21lnaxbaxbc74 b2423ln8acbxaxbcC75 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783 sindxcosxC84 i85 taxlcsx86 codniC87 sexlta()42xlnsectaxC88 cdlntClot89 2s
6、exta90 cdco91 setanxsexC92 cc93 2sidx1si24x94 conC95 sinx121sicosindxx96 cdcn97 sinx12sisinnxx98 codcoco99 sidmn1 21sicosindmnmx 2x100 sincodaxb11cos()cos()2()2()ababxC101 i in()in()()()x8102 cosdaxb11sin()sin()2()2()abxabxC103 sinabx22tarcCbb2()104 dsix22tn1laxa2()b105 cosabrctn(ta)2bbxCa2()a106 dc
7、sxt1lan2bxb2()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 2rcsindx3221rci()9C116 ao2aosx117 rcsdx22()rc44xa9118 2arcosdx3221arcos()9xaxC119 tn2tnl120 arcdx21()arctx121 2tn3322tnln()6axC（
8、十三）含有指数函数的积分122 dxa1lxC123 ea124 ax2(1)eax125 edn 1dnnx126 xa2l(l)xxaC127 dnx 11dllnxx128 esiab2e(sicos)ab129 cox xxC130 esinda 12esin(sics)anbxb22()idax131 ecosdaxnb 121ecos(sin)axnbxb22()daxn（十四）含有对数函数的积分132 lndxlxC133 l134 nx1(ln)x10135 (ln)dx1(l)(ln)dxx136 m1 1(ln)dmmx （十五）含有双曲函数的积分137 shdxcC138 139 txlnc140 2shd1sh24xC141 cx（十六）定积分142 0osdnsidnx143 0cimx144 osdn,mn145 ix0,146 0sindm0cosdmxn0,2mn147 nI20sinx20sn 1nI（ 为大于 1 的正奇数） ， 13425nI nI（ 为正偶数） ， 1 0I2换 元 积 分 法
