考研数学常用积分公式.pdf

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1、考研数学助手您考研的忠实伴侣常用积分公式（一）含有axb的积分(a0)dx11．＝lnaxbCaxba112．(axb)dx＝(axb)C（1）a(1)x13．dx＝(axbblnaxb)C2axba2x11224．dx＝(axb)2(baxb)blnaxbCaxba32dx1axb5．＝lnCxaxb()bxdx1aaxb6．＝lnC22xaxb()bxbxx1b7．dx＝(lnaxb)C22(axb)aaxb22x1b8

2、．dx＝(axb2lnbaxb)C23(axb)aaxbdx11axb9．＝lnC22xaxb()bax(b)bx（二）含有axb的积分2310．axbxd＝(axb)C3a2311．xaxbxd＝(3ax2)(baxb)C215a22222312．xaxbxd＝(15ax12abx8)(baxb)C3105ax213．dx＝(ax2)baxbC2axb3a2x222214．dx＝(3ax4abx8)baxbC3axb15a1axbblnC(

3、b0)dxbaxbb15．＝xaxb2axbarctanC(b0)bbdxaxbadx16．2＝xaxbbx2bxaxbaxbdx17．dx＝2axbbxxaxbaxbaxbadx18．dx＝2xx2xaxb22（三）含有xa的积分dx1x19．=arctanC22xaaadxx2n3dx20．=22n222n1222n1(xa)2(n1)ax(a)2(n1)a(xa)dx1xa21．=lnC22xa2axa2（四）含有ax

4、ba(0)的积分1aarctanxC(b0)dxabb22．2＝axb1axblnC(b0)2abaxbx1223．dx＝lnaxbC2axb2a2xxbdx24．dx＝22axbaaaxb2dx1x25．＝lnC22xax(b)2baxbdx1adx26．＝222xax(b)bxbaxb2dxaaxb127．＝lnC32222xax(b)2bx2bxdxx1dx28．＝2222(axb)2(baxb)2baxb2（五）含有axbx

5、c(a0)的积分22axb2arctanC(b4ac)22dx4acb4acb29．2＝2axbxc12axbb4ac2lnC(b4ac)b24ac2axbb24acx12bdx30．dx＝lnaxbxc22axbxc2a2aaxbxc22（六）含有xa(a0)的积分dxx2231．＝arshC＝ln(xxa)C22a1xadxx32．＝C223222(xa)axax2233．dx＝xaC22xax134．dx＝C22322(

6、xa)xa22xx22a2235．dx＝xaln(xxa)Cx2a2222xx2236．dx＝ln(xxa)C22322(xa)xa22dx1xaa37．＝lnCxx2a2ax22dxxa38．＝C222ax2xxa222x22a2239．xaxd＝xaln(xxa)C22223x2222342240．(xa)dx＝(2x5)axaaln(xxa)C8822122341．xxadx＝(xa)C34222x2222a2242．xxaxd＝(

7、2xa)xaln(xxa)C882222xa22xaa43．dx＝xaalnCxx2222xaxa2244．dx＝ln(xxa)C2xx22（七）含有xa(a0)的积分dxxx2245．＝archC=lnxxaC22xa1xadxx46．＝C223222(xa)axax2247．dx＝xaC22xax148．dx＝C22322(xa)xa22xx22a2249．dx＝xalnxxaCx2a2222xx2250．dx＝lnxx

8、aC22322(xa)xadx1a51．＝arccosCxx2a2ax22dxxa52．＝C222ax2xxa222x22a2253．xadx＝xalnxxaC22223x2222342254．(x