常用积分公式汇总+较全面的积分表

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1、INTEGRALSELEMENTARYFORMSZ1.adx¼axZZ2.a
fðxÞdx¼afðxÞdxZZðyÞ0dy3.ðyÞdx¼dy,wherey¼y0dxZZZ4.ðuþvÞdx¼udxþvdx,whereuandvareanyfunctionsofxZZZZ5.udv¼udvvdu¼uvvduZZdvdu6.udx¼uvvdxdxdxZxnþ17.xndx¼,exceptn¼1nþ1Zf0ðxÞdx8.¼logfðxÞ,ðdfðxÞ¼f0ðxÞdxÞfðxÞZdx9.¼logxxZf0ðxÞdxpffiffiffiffiffiffiffiffiffi10.pffiffiffiffiffiffiffiffiffi¼fðxÞ,ðdfðxÞ¼f

2、0ðxÞdxÞ2fðxÞZ11.exdx¼exZ12.eaxdx¼eax=aZbax13.baxdx¼,ðb>0ÞalogbZ14.logxdx¼xlogxxZ15.axlogadx¼ax,ða>0ÞZdx11x16.¼tana2þx2aa8>>11x>>tanhZ>>>>>:1aþx22log,ða>xÞ2aax8>>11xZ>>coth>>>:1xa22log,ðx>aÞ2axþaA-20INTEGRALS(Continued)8>>sin1xZ>>>

3、a2x2>>>>>:cos1x,ða2>x2ÞjajZdxpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi20.pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi¼logðxþx2a2Þx2a2Zdx11x21.pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi¼secxx2a2jajaZ!pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidx1aþa2x222.pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi¼logxa2x2axFORMSCONTAINING(aþbx)aþbxForformscontainingaþbx,butnotlistedinthetable,thesubstitutionu¼xmayprovehelpful.Znþ1nðaþbx

4、Þ23.ðaþbxÞdx¼,ðn6¼1Þðnþ1ÞbZn1nþ2anþ124.xðaþbxÞdx¼ðaþbxÞðaþbxÞ,ðn6¼1,2Þb2ðnþ2Þb2ðnþ1ÞZnþ3nþ2nþ12n1ðaþbxÞðaþbxÞ2ðaþbxÞ25.xðaþbxÞdx¼2aþab3nþ3nþ2nþ18mþ1nZ>>xðaþbxÞanmn1>>þxðaþbxÞdx>>mþnþ1mþnþ1>>>>>>orZ>><Zmn1xmþ1ðaþbxÞnþ1þðmþnþ2ÞxmðaþbxÞnþ1dx26.xðaþbxÞdx¼>>aðnþ1Þ>>>>>>or>>>>Z>>:1mnþ1m1nxða

5、þbxÞmaxðaþbxÞdxbðmþnþ1ÞZdx127.¼logðaþbxÞaþbxbZdx128.¼ðaþbxÞ2bðaþbxÞZdx129.¼32ðaþbxÞ2bðaþbxÞ81>>>>½aþbxalogðaþbxÞZ>>>>>:xalogðaþbxÞbb2A-21INTEGRALS(Continued)Zxdx1a31.¼logðaþbxÞþðaþbxÞ2b2aþbxZxdx11a32.ðaþbxÞn¼b2n2þn1,n6¼1,2ðn2ÞðaþbxÞðn1ÞðaþbxÞZx2dx1133.¼ðaþbxÞ22aðaþb

6、xÞþa2logðaþbxÞaþbxb32Zx2dx1a234.¼aþbx2alogðaþbxÞðaþbxÞ2b3aþbxZx2dx12aa235.¼logðaþbxÞþðaþbxÞ3b3aþbx2ðaþbxÞ2Zx2dx112aa236.ðaþbxÞn¼b3n3þn2n1,n6¼1,2,3ðn3ÞðaþbxÞðn2ÞðaþbxÞðn1ÞðaþbxÞZdx1aþbx37.¼logxðaþbxÞaxZdx11aþbx38.¼logxðaþbxÞ2aðaþbxÞa2xZ"#2dx112aþbxx39.¼þlogxðaþbxÞ3a32aþbxaþbxZdx1

7、baþbx40.¼þlogx2ðaþbxÞaxa2xZdx2bxab2x41.¼þlogx3ðaþbxÞ2a2x2a3aþbxZdxaþ2bx2baþbx42.¼þlogx2ðaþbxÞ2a2xðaþbxÞa3x2222FORMSCONTAININGcx,xcZdx11x43.¼tanc2þx2ccZdx1cþx2244.¼log,ðc>xÞc2x22ccxZdx1xc2245.