高等数学积分公式大全.docx

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1、常用积分公式（一）含有axb的积分(a0)1．dx＝1lnaxbCaxba2．(axb)dx＝a(11)(axb)1C（1）3．axxdx＝12(axbblnaxb)Cba4．x2dx＝11(axb)22b(axb)b2lnaxbCaxba325．dxb)＝1lnaxbCx(axbx6．2dxb)＝1a2lnaxbCx(axbxbxx2dx＝1b)C7．(axb)a2(lnaxbaxb8．(axx22dx＝13(axb2blnaxbb2)Cb)aaxb9．dx11axbCx(axb)2＝b)b2lnxb(ax（二）含有axb的积分10．axbd

2、x＝2(axb)3C3a211．xaxbdx＝2(3ax2b)(axb)3C15a12．x2axbdx＝23(15a2x212abx8b2)(axb)3C105a13．xdx＝2(ax2b)axbCaxb3a214．x2＝2222axbdx15a3(3ax4abx8b)axbC1axbbC(b0)dxlnaxbb15．＝baxxb2arctanaxbC(b0)bb16．dx＝axbadx2axbx2bxaxbxb17．axbdx＝2axbbdxbxxax18．axbdx＝axbadxbx2x2xax（三）含有x2a2的积分19．dx=1xC2a

3、2arctanxaa20．dxn=x2n3dx2a2)2(x22)n12(n1)a2(x2a2)n1(x2(n1)aa21．dx=1xaC2a2lnxax2a（四）含有ax2b(a0)的积分1arctanaxC(b0)22．dxabbb＝axbax21lnC(b0)2abaxb23．xdx＝1lnax2bCax2b2a24．x2dx＝xbdx2aaax2baxb25．dx＝1lnx2bCx(ax2b)2bax226．dx＝1adx2(ax2b)bxbax2bxdxaax2b1C27．3(ax2b)＝2lnx22x2b2bx28．dx＝x1dxb

4、)b)2bax2b(ax222b(ax2（五）含有ax2bxc(a0)的积分2arctan2axbC(b24ac)29．dx＝4acb24acb2bx12axbb24acax2cln(b24ac)b24ac2axbb2C4ac30．xcdx＝1lnax2bxcbax2dxax2bx2a2abxc（六）含有x2a2(a0)的积分31．dxa2＝arshxC1＝ln(xx2a2)Cx2a32．dx＝xC(x2a2)3a2x2a233．xa2dx＝x2a2Cx234．xdx＝1C(x2a2)3x2a235．x2dx＝xx2a2a2ln(xx2a2)C

5、x222a236．(x2x223dx＝x2xa2ln(xx2a2)Ca)37．dxa2＝1lnx2a2aCxx2ax38．dx＝x2a2Cx2a2xx2a239．x2a2dx＝xx2a2a2ln(xx2a2)C2240．(x2a2)3dx＝x(2x25a2)x2a23a4ln(xx2a2)Ca2dx＝18841．xx2(x2a2)3C342．x2x2a2dx＝x(2x843．x2a2dx＝x2ax2a2)x2a2a4x2a2)Cln(x82alnx2a2aCx44．x2a2dx＝x2a2ln(xx2a2)Cx2x（七）含有x2a2(a0)的积

6、分45．dx＝xarchxC1=lnxx2a2Cx2a2xa46．dx＝xC(x2a2x2a2)3a247．xa2dx＝x2a2Cx248．xdx＝1C(x2x2a2a2)349．x2a2dx＝xx2a2a2lnxx2a2Cx22250．x2dx＝xa2lnxx2a2C(x2a2)3x251．dx＝1arccosaCxx2a2ax52．dx＝x2a2Ca2xx2x2a253．x2a2dx＝xx2a2a2lnxx2a2C2254．(x2a2)3dx＝x(2x25a2)x2a23a4lnxx2a2Ca2dx＝18855．xx2(x2a2)3C356

7、．x2x2a2dx＝x(2x2a2)x2a2a4lnxx2a2C8857．x2a2dx＝x2a2aarccosaCxx58．x2a2dx＝x2a2lnxx2a2Cx2x（八）含有a2x2(a0)的积分59．dxx2＝arcsinxCa2a60．dx＝xC(a2x2)3a2a2x261．a2xdx＝a2x2Cx262．xdx＝1C(a2x2)3a2x263．x2dx＝xa2x2a2arcsinxCa2x222a64．x2dx＝xx2arcsinxC(a2x2)3a2a65．dx＝1lnaa2x2Cxa2x2ax66．dx＝a2x2Cx2a2x2a

8、2x67．a2x2dx＝xa2x2a2arcsinxC22a68．(a2x2)3dx＝x(5a22x2)a2x23a4arcsinxC88a69．xa