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时间:2020-03-26
《高等数学积分公式大全.pdf》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、常用积分公式(一)含有axb的积分(a0)dx11.=lnaxbCaxba112.(axb)dx=(axb)C(1)a(1)x13.dx=(axbblnaxb)C2axba2x11224.dx=(axb)2(baxb)blnaxbCaxba32dx1axb5.=lnCxax(b)bxdx1aaxb6.=lnC22xax(b)bxbxx1b7.dx=(lnaxb)C22(axb)aaxb22x1b8.dx=(axb2lnbaxb)C23(axb)
2、aaxbdx11axb9.=lnC22xax(b)bax(b)bx(二)含有axb的积分2310.axbxd=(axb)C3a2311.xaxbxd=(3ax2)(baxb)C215a22222312.xaxbxd=(15ax12abx8)(baxb)C3105ax213.dx=(ax2)baxbC2axb3a2x222214.dx=(3ax4abx8)baxbC3axb15a1axbblnC(b0)dxbaxbb15.=xaxb2axbarctanC(b0)b
3、bdxaxbadx16.2=xaxbbx2bxaxbaxbdx17.dx=2axbbxxaxbaxbaxbadx18.dx=2xx2xaxb22(三)含有xa的积分dx1x19.=arctanC22xaaadxx2n3dx20.=22n222n1222n1(xa)2(n1)ax(a)2(n1)a(xa)dx1xa21.=lnC22xa2axa2(四)含有axba(0)的积分1aarctanxC(b0)dxabb22.=2axb1axblnC(b0)2
4、abaxbx1223.dx=lnaxbC2axb2a2xxbdx24.dx=22axbaaaxb2dx1x25.=lnC22xax(b)2baxbdx1adx26.=222xax(b)bxbaxb2dxaaxb127.=lnC32222xax(b)2bx2bxdxx1dx28.=2222(axb)2(baxb)2baxb2(五)含有axbxc(a0)的积分22axb2arctanC(b4ac)22dx4acb4acb29.=22axbxc12axbb4ac2lnC
5、(b4ac)b24ac2axbb24acx12bdx30.dx=lnaxbxc22axbxc2a2aaxbxc22(六)含有xa(a0)的积分dxx2231.=arshC=ln(xxa)C22a1xadxx32.=C223222(xa)axax2233.dx=xaC22xax134.dx=C22322(xa)xa22xx22a2235.dx=xaln(xxa)Cx2a2222xx2236.dx=ln(xxa)C22322(xa)xa22dx1xaa37.=l
6、nCxx2a2ax22dxxa38.=C222ax2xxa222x22a2239.xadx=xaln(xxa)C22223x2222342240.(xa)dx=(2x5)axaaln(xxa)C8822122341.xxadx=(xa)C34222x2222a2242.xxadx=(2xa)xaln(xxa)C882222xa22xaa43.dx=xaalnCxx2222xaxa2244.dx=ln(xxa)C2xx22(七)含有xa(a0)的积分dxxx2245.
7、=archC=lnxxaC22xa1xadxx46.=C223222(xa)axax2247.dx=xaC22xax148.dx=C22322(xa)xa22xx22a2249.dx=xalnxxaCx2a2222xx2250.dx=lnxxaC22322(xa)xadx1a51.=arccosCxx2a2ax22dxxa52.=C222ax2xxa222x22a2253.xadx=xalnxxaC22223x2222342254.(xa)dx=(2x5)ax
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