积分公式大全文档格式.docx

积分公式大全文档格式.docx

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积分公式大全积分公式大全常用积分公式4.-一X=-A3卩（ax+b）2-2b（ax+b）+b2lnax+b+Caxba2fdx=1lnax+b+CJlnx（ax+b）bX5.

（二）含有.axb的积分10.Jax+bdx=2J（a+b）3+CL3a11.x、.axbdx=飞（3ax-2b）（axb）3C15a12.2.axbdx=2（15a22-12abx8b2）.（axb）3C105a13.JXd=-2y（ax-2b）0x+b+CaXb3a15.dxXMaxb2、-baxb:

@#@-b（b0）（b：

@#@0）.axb-.b.aXbb（三）含有x2-a2的积分.dx1X19.-22=arctan一Cx2+a2aaFdxX2n3FdX20=22、n2,22、n42.,22、n_J21.dx=X-a12aInra（Xa）2（n-1）a（Xa）2（n-1）a（Xa）rdxJaretaab晶+c（bA0）IaXHbJln2-abC（beO）+V-b2（四）含有axb（a0）的积分22.X1223.12dx=lnax+b+Cax+b2a24.X2dXaxbdx2axb25.dxx（ax2b）丄In2b2Xax2b26.ILdxx2（ax2b）1bx27.dx3x3（ax2b）2b228.29.30.（A）31.32.33.dxbax2bax2bx2rdx222I（axb）2b（axb）2bax2bdx2-含有ax2bxc（a0）的积分ILdxax2bxC-arctan2JC4ac-b2In、b2-4ac戶dx=axbxC2a.4ac_b22axb-,b2-4ac2axb.b2-4acdx2_2（b：

@#@4ac）C（b24ac）Ina2+bx+c.22aax“+bx+c含有.X2a2（a0）的积分dx-x2a2dx.（x2a2）3arshC1=In（x.x2a2）CaaCxa2dx=x2a2C1dx=-=C.（x2a2）3x2a235.36.37.38.39.40.41.42.43.44.45.46.47.,x2aXr22a22=dx=.xaln（x.Xa）C22222、3dX=2flnXX）C（X2a2）X-adxxix2a2a1.x2a2-a=InC2dxx2,x2a2rdx=?

@#@|n（x.rCj（x2a2）3dx=-（2x25a2）.x2a2-3a4ln（x8Cj2+a2dx=L322、3x2x2a2dx=xs2-2（2xa）x2a2ln（Xx2XdX=JK+aln迂aa+C222a2）Ca2）C-dx三x2a2In（xx2a2）C含有.2-a2（a0）的积分dX22X-adX=archX+C1=InX+寸x2_a2+CX2-a2）322dX=2_a2C48.49.50.51.52.53.54.55.56.57.58.（A）59.60.PdX=-.212+C-a）.x-aX*2jl22XrX-a2IXr2TaIdx=X-aIn2XIXx-a21=arccosaXdx222.,口dx=号lnC2X（X2_a2）3dx=xX（225a2）、2_a8ILj2-a2dx=IJ（X2_a2）3+CL3+3a4nX8+4a2+Cx2、FdX=j22-血F4-lnx+Px-a+C8Vx2-a2-aarccosa22.X-a.dx=X-22X-aI2dx=X22X-a+Inx+2-a2含有.a2-x2（a0）的积分dxa2=2X=arcsnCadx.（a2-X2）3-+c222aa-X61.62.63.64.65.66.67.68.69.70.71.72.（九）73.J/22dx=-da2x2+cI.dx=.（a2-x2）31+C.a2-x2,a-X2f,Xdx=JIl22.a-X2X22ax.a-XarcsInC22aIX.Xdx1I=lna2-x2a;@#@22ya-X+cdxx2.a2-x22Ja2-x2dx=XJa2_x2+arcsin+C22a!

@#@；@#@（a2_x2）3dx=；@#@（5a2_2x2）.a2_x2Jxa7dx=一3JU-a4arcsinXC8a42-a2-2dx=（22-a2）、a2-2-arcsinC88a22adx=、a2x2alnXJ22a_aXC_22-22axa-xXC2dx=arcsInCXXa含有-ax2bxc（a0）的积分dx=丄.ax2bxcIaIn2ax+b+2寸aJax2+bx+c+C74.22axb-2axbxCdX=axbxC4a4ac-b18苛l2xb2aaxbxCC75.ax2bxCdx=丄Ja2+bx+ca22xb2a76.dxICbx-a212ax-barcsin:

@#@2+Ca,b4ac77.Cbx-ax2dx2ax一b2bx-a24ab24ac.2ax-barcsInC8ab24ac78.-dx-Cbx-axIJC+bx-a2a+Aarcsin卓+C2a3-b24ac或、.（xa）（bx）的积分81.82.79.80.含有*兰（X一b）JbWa）In（J（b-a）arcsinI-_+Cb-x（x-b）x-ab-xXa+x_b）+c,（x-a）（b-x）2arcsin+C（acb）.（x-a）（b_x）d2xa-bX=（x-a）（b-x）+守arcsin后+C（a：

@#@b）（十一）含有三角函数的积分83.Sinxdx=-CoSXC84.85.86.87.88.89.90.91.92.93.94.95.96.97.98.99.100.CoSXdX=SinxCILtanXdX=Incosx+CcotXdX=lnSinx+CJTXsecxdx=lntan（上+）+C=lnsecx+tanx+C42Xfcscxdx=lntan+c=lncscxcotx+CL22SeCXdX=tanxCCSCXdX=-cotXCSeCXtanXdX=SeCXCCSCXcotXdX=-CSCXCsin12XdX=X1sin2xC242X1cosXdX=Sin2xCSinndXdX24cosnXdX1n4.n-1cosXSinxCOSnXdXnndx1cosxn-2dxnSinXn-1n4SinXn-1!

@#@n_2SinXdx1SinXn-2dxnn-1+n-2cosXcosXnJAcosXnTSinnXdX=-丄Sinn4xcosxn-nnI-mnIcosXSinXdXm-1n十cosXSinXI-m-2nIcosXSinXdXmn-2IcosXSinXdXSinaxCOSbXdX=-12（ab）cos（ab）x-12（a-b）cos（a-b）xSinaxSinbxdx=cosaxCOSbXdX=12（ab）12（ab）sin（ab）xsin（ab）x12（a-b）12（a-b）Sin（a-b）xSin（ab）XC101.102.103.104.105.106.107.108.109.110.111.112.Xatanb22arctanCab.a-b上叫I:

@#@二;@#@Xabtan2lb-afdxa2cos2Xb2sin2Xabfdx.222-2-acosx-bSinX丄ln2abbtanxabtanx-adxlnababcosx11XSinaxdx=2SinaxXcosaxCaa2.2+2+2+qXSinaxdx=Xcosax2xsInaX亍cosaxCaaa11XCOSaXdX=2cosaxXSinaxCaax2COSaXdX=1x2sinaxWxcosax-sinaxCaaa（十二）含有反三角函数的积分（其中a0）XXf22113.arcsindx=XarCSina-xCaa22,.XXa、.XX口2C114.XarCSIndx=（）arcsna-XCa24a43dXX12222=arcsIn（X2a）、a-XC3a9118.x2arccos二dx=arccosx-l（x22a2）,a2-x2Ca3a9119.arctanxdx=Xarctan-aln（a2x2）Caa2X122Xa120.XarCtandx=（aX）arctanXCa2a2332XXXa2a22121.Xarctandx=arctanXln（aX）Ca3a66（十三）含有指数函数的积分122.123.124.125.126.127.128.129.1axdx=axClnaax1axedx=eCaXeaXdX=-12（ax-1）eaxCanax1naxnn4ax.XedX=XeXedXaaLXaXdX=ax12axClna（lna）XnaXdX=1nXalnaeaxSinbxdx=eaxcosbxdx=nn4XIXadXlna1a2b2eax（asinbx-bcosbx）C1a2b2eax（bsinbxaCOSbX）C138.ChXdX=ShXC（十四）含有对数函数的积分139.thxdx=InChXC140.sh2xdx=-X-sh2xC24r2XI1丄141.ChXdX=sh2xC4（十六）定积分142.cosnxdx=Sinnxdx=0-.143.COSmXSinnxdx=0-二0,mn144.COSmXCOSnxdx=I,m=n-0,m=n145.SinmXSinnxdx=入:

@#@,m=n146.卩，Sinmxsinnxdx=COSmXCOSnxdx=LOI,m=n2147.InO2SinnXdX=02CoSnXdXInn-1In1n_2Inn-3.n-2n-3（n为大于1的正奇数），Ii=1n-2Jl422（n为正偶数）ln.X-ax2.,x2_a21m.n4丄n1cosXSinXmnmn