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1、08070141常用导数和积分公式导数公式：基本积分表：三角函数的有理式积分：axxaaactgxxxtgxxxxctgxxtgxaxxln1)(logln)(csc)(cscsec)(seccsc)(sec)(22222211)(11)(11)(arccos11)(arcsinxarcctgxxarctgxxxxxCaxxaxdxCshxchxdxCchxshxdxCaadxaCxctgxdxxCxdxtgxxCctgxxdxxdxCtgxxdxxdxxx)ln(lncsccscsecseccscsinseccos22222222CaxxadxCxaxaaxadxCaxaxaaxdxCaxa
2、rctgaxadxCctgxxxdxCtgxxxdxCxctgxdxCxtgxdxarcsinln21ln211csclncscseclnsecsinlncosln22222222CaxaxaxdxxaCaxxaaxxdxaxCaxxaaxxdxaxInnxdxxdxInnnnarcsin22ln22)ln(221cossin222222222222222222222020名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页，共 13 页 - - - - - - - - - 080
3、70141常用导数和积分公式222212211cos12sinududxxtguuuxuux，（一）含有axb的积分 (0a)1dxaxb1ln axbCa2() daxbx11()(1)axbCa（1）3dxxaxb21(ln)axbbaxbCa42dxxaxb22311()2 ()ln2axbb axbbaxbCa5d()xx axb1lnaxbCbx62d()xxaxb21lnaaxbCbxbx72d()xxaxb21(ln)baxbCaaxb822d()xxaxb231(2 ln)baxbbaxbCaaxb92d()xx axb211ln()axbCb axbbx（二）含有axb的积分
4、10daxb x32()3axbCa11dx axb x322(32 )()15axbaxbCa122dxaxb x222332(15128)()105a xabxbaxbCa13dxxaxb22(2 )3axbaxbCa名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式142dxxaxb22232(348)15a xabxbaxbCa15dxx axb1ln(0)2arctan(0)axbbC
5、bbaxbbaxbCbbb162dxxaxbd2axbaxbxbx axb17daxbxxd2xaxbbxaxb182daxbxxd2axbaxxx axb（三）含有22xa的积分1922dxxa=1arctanxCaa2022d()nxxa=2221222123d2(1)()2(1)()nnxnxnaxanaxa2122dxxa=1ln2xaCaxa（四）含有2(0)axb a的积分222dxaxb1arctan(0)1ln(0)2axCbbabaxbCbabaxb232dxxaxb21ln2axbCa名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - -
6、- - - - - - 名师精心整理 - - - - - - - 第 3 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式2422dxxaxb2dxbxaaaxb252d()xx axb221ln2xCbaxb2622d()xxaxb21daxbxbaxb2732d()xxaxb22221ln22axbaCbxbx2822d()xaxb221d2 ()2xxb axbbaxb（五）含有2axbxc (0)a的积分292dxaxbxc222222222arctan(4)44124ln(4)424axbCbacacbacbaxbbacCbacbacaxbba
7、c302dxxaxbxc221dln22bxaxbxcaaaxbxc（六）含有22xa(0)a的积分3122dxxa1arshxCa22ln()xxaC32223d()xxa222xCaxa3322dxxxa22xaC34223d()xxxa221Cxa名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式35222dxxxa22222ln()22xaxaxxaC362223d()xxxa2222l
8、n()xxxaCxa3722dxxxa221lnxaaCax38222dxxxa222xaCa x3922dxax22222ln()22xaxaxxaC40223() dxax22224223(25)ln()88xxaxaaxxaC4122dxxax2231()3xaC42222dxxax4222222(2)ln()88xaxaxaxxaC4322dxaxx2222lnxaaxaaCx44222dxaxx2222ln()xaxxaCx（七）含有22xa(0)a的积分4522dxxa1archxxCxa=22ln xxaC46223d()xxa222xCaxa4722dxxxa22xaC名师资料
9、总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式48223d()xxxa221Cxa49222dxxxa22222ln22xaxaxxaC502223d()xxxa2222lnxxxaCxa5122dxxxa1arccosaCax52222dxxxa222xaCa x5322dxax22222ln22xaxaxxaC54223() dxax22224223(25)ln88xxaxaaxxaC5522d
10、xxax2231()3xaC56222dxxax4222222(2)ln88xaxaxaxxaC5722dxaxx22arccosaxaaCx58222dxaxx2222lnxaxxaCx（八）含有22ax(0)a的积分5922dxaxarcsinxCa60223d()xax222xCaax名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 6 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式6122dxxax22axC62223d()xxax22
11、1Cax63222dxxax222arcsin22xaxaxCa642223d()xxax22arcsinxxCaax6522dxx ax221lnaaxCax66222dxxax222axCa x6722daxx222arcsin22xaxaxCa68223() daxx222243(52)arcsin88xxaxaxaCa6922dx axx2231()3axC70222dxaxx42222(2)arcsin88xaxxaaxCa7122daxxx2222lnaaxaxaCx72222daxxx22arcsinaxxCxa（九）含有2axbxc(0)a的积分732dxaxbxc21ln 2
12、2axbaaxbxcCa名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 7 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式742daxbxc x224axbaxbxca2234ln 228acbaxbaaxbxcCa752dxxaxbxc21axbxca23ln 222baxbaaxbxcCa762dxcbxax212arcsin4axbCabac772dcbxaxx2232242arcsin484axbbacaxbcbxaxCaabac78
13、2dxxcbxax23212arcsin24baxbcbxaxCaabac（十）含有xaxb或()()xa bx的积分79dxaxxb()()ln()xaxbbaxaxbCxb80dxaxbx()()arcsinxaxaxbbaCbxbx81d()()xxabx2arcsinxaCbx()ab82()()dxa bxx22()()()arcsin44xabbaxaxabxCbx()ab（十一）含有三角函数的积分83sin dx xcosxC名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - -
14、第 8 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式84cos dx xsin xC85tan dx xln cosxC86cot dx xln sin xC87sec dx xln tan()42xCln sectanxxC88csc dx xln tan2xCln csccotxxC892secdx xtanxC902cscdx xcot xC91sec tan dxx xsecxC92csc cot dxx xcscxC932sindx x1sin 224xxC942cosdx x1sin224xxC95sindnx x1211sincossi
15、ndnnnxxx xnn96cosdnx x1211cossincosdnnnxxx xnn97dsinnxx121cos2d1 sin1sinnnxnxnxnx98dcosnxx121sin2d1 cos1cosnnxnxnxnx99cossindmnxx x11211cossincossindmnmnmxxxx xmnmn11211cossincossindmnmnnxxxx xmnmn100sincosdaxbx x11cos()cos()2()2()ab xab xCabab名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - -
16、 名师精心整理 - - - - - - - 第 9 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式101sinsindaxbx x11sin()sin()2()2()ab xab xCabab102coscosdaxbx x11sin()sin()2()2()ab xab xCabab103dsinxabx2222tan22arctanxabCabab22()ab104dsinxabx222222tan12lntan2xabbaCxbaabba22()ab105dcosxabx2arctan(tan)2ababxCababab22()ab106dcos
17、xabxtan12lntan2xababbaCabbaxabba22()ab1072222dcossinxaxbx1arctan(tan)bxCaba1082222dcossinxaxbx1tanln2tanbxaCabbxa109sindxax x211sincosaxxaxCaa1102sindxax x223122cossincosxaxxaxaxCaaa111cosdxax x211cossinaxxaxCaa1122cosdxax x223122sincossinxaxxaxaxCaaa（十二）含有反三角函数的积分（其中0a）113arcsindxxa22arcsinxxaxCa名师
18、资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 10 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式114arcsindxxxa2222()arcsin244xaxxaxCa1152arcsindxxxa322221arcsin(2)39xxxaaxCa116arccos dxxa22arccosxxaxCa117arccos dxxxa2222()arccos244xaxxaxCa1182arccosdxxxa322221arccos(2)39
19、xxxaaxCa119arctandxxa22arctanln()2xaxaxCa120arctandxxxa221()arctan22xaaxxCa1212arctandxxxa33222arctanln()366xxaaxaxCa（十三）含有指数函数的积分122dxax1lnxaCa123e daxx1eaxCa124e daxxx21(1)eaxaxCa125e dnaxxx11ee dnaxnaxnxxxaa126dxxax21ln(ln)xxxaaCaa127dnxx ax11dlnlnnxnxnx axaxaa128esindaxbx x221e ( sincos)axabxbbx
20、Cab129ecosdaxbx x221e ( sincos)axbbxabxCab名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 11 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式130esindaxnbx x12221esin( sincos)axnbx abxnbbxab n22222(1)esindaxnn nbbx xab n131ecosdaxnbx x12221ecos(cossin)axnbx abxnbbxab n2222
21、2(1)ecosdaxnn nbbx xab n（十四）含有对数函数的积分132lndx xlnxxxC133dlnxxxln ln xC134lndnxx x111(ln)11nxxCnn135(ln) dnxx1(ln)(ln)dnnxxnxx136(ln) dmnxxx111(ln)(ln)d11mnmnnxxxxxmm（十五）含有双曲函数的积分137sh dx xchxC138ch dx xshxC139th dx xlnchxC1402shdx x1sh224xxC1412chdx x1sh224xxC（十六）定积分142cosdnx xsindnx x0 143cossindmxn
22、x x0 144coscosdmxnx x0,mnmn名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 12 页，共 13 页 - - - - - - - - - 08070141常用导数和积分公式145sinsindmxnx x0,mnmn1460sinsindmxnx x0coscosdmxnx x0,2mnmn147nI20sindnx x20cosdnx xnI21nnIn134 225 3nnnInnL（n为大于 1 的正奇数），1I1 133 124 2 2nnnInnL（n为正偶数），0I2名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 13 页，共 13 页 - - - - - - - - -