普通积分表资料大全.doc

|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)15axbC|15 dxab1ln(0)2arctxbCb16 2x dxbxab17 dabxax18 2 d2bab（三）含有 的积分xa19 =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()ab2221lnaxbC|28 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 23d()x21xa35 2xa222ln()xaC36 23d()22l()xa37 2xa1lnC38 22dx2xa39 a222ln()xaC40 23()dx22423(5)ln()88xaxa41 a31C|42 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()x22423(5)ln88xxa55 da31a56 22xx4222()ln88axxaC|57 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 22lnax|72 2dax2arcsinxC（九）含有 的积分2b(0)73 2dxac 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|83 sindxcosxC84 i85 taxlcsx86 codniC87 sexlta()42xlnsectaxC88 cdlntClot89 2sexta90 cdco91 setanxsexC92 cc93 2sidx1si24x94 conC95 sinx121sicosindxx96 cdcn97 sinx12sisinnxx98 codcoco99 sidmn1 21sicosindmnmx 2x100 sincodaxb11cos()cos()2()2()ababxC101 i in()in()()()x|102 cosdaxb11sin()sin()2()2()abxabxC103 sinabx22tarcCbb2()104 dsix22tn1laxa2()b105 cosabrctn(ta)2bbxCa2()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()arsin44xa115 2rcsindx3221rci()9C116 ao2aosx117 rcsdx22()rc44xa|118 2arcosdx3221arcos()9xaxC119 tn2tnl120 arcdx21()arctx121 2tn3322tnln()6axC（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)x|135 (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