高等数学常用积分公式查询表.pdf

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1、.导数公式：12(arcsinx)(tgx)secx21x2(ctgx)cscx1(arccosx)(secx)secxtgx21x(cscx)cscxctgx1xx(arctgx)2(a)alna1x11(logax)(arcctgx)2xlna1x基本积分表：tgxdxlncosxCdx2secxdxtgxC2cosxctgxdxlnsinxCdx2cscxdxctgxC2secxdxlnsecxtgxCsinxsecxtgxdxsecxCcscxdxlncscxctgxCcscxctgxdxcscxCdx1xar

2、ctgC22xaxaaxaadxCdx1xalnalnC22xa2axashxdxchxCdx1ax22lnCchxdxshxCax2aaxdxxdx22arcsinCln(xxa)C2222axaxa22nnn1InsinxdxcosxdxIn200n222x22a22xadxxaln(xxa)C22222x22a22xadxxalnxxaC22222x22axaxdxaxarcsinC22a三角函数的有理式积分：..22u1ux2dusinx2，　cosx2，　utg，　dx21u1u21u（一）含有axb的积分(

3、a0)dx11．＝lnaxbCaxba112．(axb)dx＝(axb)C（1）a(1)x13．dx＝(axbblnaxb)C2axba2x11224．dx＝(axb)2b(axb)blnaxbC3axba2dx1axb5．＝lnCx(axb)bxdx1aaxb6．＝lnC22x(axb)bxbxx1b7．dx＝(lnaxb)C22(axb)aaxb22x1b8．dx＝(axb2blnaxb)C23(axb)aaxbdx11axb9．＝lnC22x(axb)b(axb)bx（二）含有axb的积分2310．axbdx＝(

4、axb)C3a2311．xaxbdx＝(3ax2b)(axb)C215a22222312．xaxbdx＝(15ax12abx8b)(axb)C3105ax213．dx＝(ax2b)axbC2axb3a..2x222214．dx＝(3ax4abx8b)axbC3axb15a1axbblnC(b0)dxbaxbb15．＝xaxb2axbarctanC(b0)bbdxaxbadx16．＝2xaxbbx2bxaxbaxbdx17．dx＝2axbbxxaxbaxbaxbadx18．dx＝2xx2xaxb22（三）含有xa的积分d

5、x1x19．=arctanC22xaaadxx2n3dx20．=22n222n1222n1(xa)2(n1)a(xa)2(n1)a(xa)dx1xa21．=lnC22xa2axa2（四）含有axb(a0)的积分1aarctanxC(b0)dxabb22．＝2axb1axblnC(b0)2abaxbx1223．dx＝lnaxbC2axb2a..2xxbdx24．2dx＝2axbaaaxb2dx1x25．＝lnC22x(axb)2baxbdx1adx26．＝222x(axb)bxbaxb2dxaaxb127．＝lnC322

6、22x(axb)2bx2bxdxx1dx28．＝2222(axb)2b(axb)2baxb2（五）含有axbxc(a0)的积分22axb2arctanC(b4ac)22dx4acb4acb29．＝22axbxc12axbb4ac2lnC(b4ac)22b4ac2axbb4acx12bdx30．dx＝lnaxbxc22axbxc2a2aaxbxc22（六）含有xa(a0)的积分dxx2231．＝arshC1＝ln(xxa)C22axadxx32．＝C223222(xa)axax2233．dx＝xaC22xax134．dx

7、＝C22322(xa)xa..22xx22a2235．dx＝xaln(xxa)C2222xa2xx2236．dx＝ln(xxa)C22322(xa)xa22dx1xaa37．＝lnC22xxaax22dxxa38．＝C2222xxaax222x22a2239．xadx＝xaln(xxa)C22223x2222342240．(xa)dx＝(2x5a)xaaln(xxa)C8822122341．xxadx＝(xa)C34222x2222a2242．xxadx＝(2xa)xaln(xxa)C882222xa22xaa43．d

8、x＝xaalnCxx2222xaxa2244．dx＝ln(xxa)C2xx22（七）含有xa(a0)的积分dxxx2245．＝archC1=lnxxaC22xaxadxx46．＝C223222(xa)axax2247．dx＝xaC22xa..x148．dx＝C22322(xa)xa22xx22a2249．dx＝xalnxxaC22