高等數(shù)學(xué)積分公式大全

高等數(shù)學(xué)積分公式大全高等數(shù)學(xué)積分公式大全高等數(shù)學(xué)積分公式大全合用標(biāo)準(zhǔn)文檔常用積分公式（一）含有axb的積分(a0)1．dx＝1lnaxbCaxba2．(axb)dx＝a(11)(axb)1C（1）3．xbdx＝12(axbblnaxb)Caxa4．x2dx＝11(axb)22b(axb)b2lnaxbCaxba325．dx＝1lnaxbCx(axb)bx6．2dxb)＝1a2lnaxbCx(axbxbx7．(axxdx＝1(lnaxbaxb)Cb)2a2b8．x22dx＝13(axb2blnaxbb2)C(axb)aaxbdx11axb9．x(axb)2＝b(axb)b2lnxC（二）含有axb的積分10．a(chǎn)xbdx＝2(axb)3C3a211．xaxbdx＝2(3ax2b)(axb)3C15a12．x2axbdx＝23(15a2x212abx8b2)(axb)3C105a13．xdx＝2(ax2b)axbCaxb3a2優(yōu)秀文案合用標(biāo)準(zhǔn)文檔14．x2＝2222axbdx15a3(3ax4abx8b)axbC1axbbC(b0)dxlnaxbb15．＝bxaxb2arctanaxbC(b0)bb16．dx＝axbadxx2axbx2bxaxbb17．a(chǎn)xbdx＝2axbbdxbxxax18．a(chǎn)xbdx＝axbadxbx2x2xax（三）含有x2a2的積分19．dx=1xCx2a2arctanaadxx2n3dx20．(x2a2)n=2(n1)a2(x2a2)n12(n1)a2(x2a2)n121．xdx=1lnxaC2a22axa（四）含有ax2b(a0)的積分1arctanaxC(b0)22．dxabbax2b＝axb1lnC(b0)2abaxb23．xdx＝1lnax2bCax2b2a優(yōu)秀文案合用標(biāo)準(zhǔn)文檔24．x2dx＝xbdxax2aa2bbax25．dx＝1lnx2bCx(ax2b)2bax226．dx＝1adxx2(ax2b)bxbax2bdxb)＝aax2b1C27．x3(ax22b2lnx22bx228．dx＝x1dx(ax2b)b)2bax2b22b(ax2（五）含有ax2bxc(a0)的積分2arctan2axbC(b24ac)29．dx＝4acb24acb2ax2bx12axbb24accln(b24ac)b24ac2axbb2C4ac30．a(chǎn)xxcdx＝1lnax2bxcbax2dx2bx2a2abxc（六）含有x2a2(a0)的積分31．dxa2＝arshxC1＝ln(xx2a2)Cx2a32．dx＝xC(x2a2)3a2x2a233．xa2dx＝x2a2Cx234．xdx＝1C(x2x2a2a2)3優(yōu)秀文案合用標(biāo)準(zhǔn)文檔35．x2dx＝xx2a2a2ln(xx2a2)Cx222a236．x2a2)3dx＝xa2ln(xx2a2)C(x2x237．dx＝1lnx2a2aCxx2a2ax38．dx＝x2a2C2x2a2a2xx39．x22dx＝x2a2a2x2a2)Caxln(x2240．(x2a2)3dx＝x(2x25a2)x2a23a4ln(xx2a2)C8841．xx2a2dx＝1(x2a2)3C342．x2x2a2dx＝x(2x843．x2a2dx＝x2ax

2a2)x2a2a4ln(xx2a2)C82alnx2a2aCx44．x2a2dx＝x2a2ln(xx2a2)Cx2x（七）含有x2a2(a0)的積分45．dx＝xarchxC1=lnxx2a2Cx2a2xa46．dx＝xC(x2a2x2a2)3a247．xa2dx＝x2a2Cx2優(yōu)秀文案合用標(biāo)準(zhǔn)文檔48．xdx＝1C(x2x2a2a2)349．x2a2dx＝xx2a2a2lnxx2a2Cx22250．x2dx＝xlnxx2a2C(x2x2a2a2)351．dx＝1arccosaCxx2a2ax52．dx＝x2a2C2x2a2a2xx53．x2a2dx＝xx2a2a2lnxx2a2C2254．(x2a2)3dx＝x(2x25a2)x2a23a4lnxx2a2Ca2dx＝18855．xx2(x2a2)3C356．x2x2a2dx＝x2a2)x2a2a4lnxx2a2C(2x8857．x2xa2dx＝x2a2aarccosaCx58．x2a2dx＝x2xa2lnxx2a2Cx2（八）含有a2x2(a0)的積分59．dxx2＝arcsinxCa2a60．dx＝xC(a2x2x2)3a2a2優(yōu)秀文案合用標(biāo)準(zhǔn)文檔61．a(chǎn)2xdx＝a2x2Cx262．xdx＝1C(a2x2)3a2x263．x2dx＝xa2x2a2arcsinxCa2x222a64．x2dx＝xx2arcsinxC(a2x2)3a2a65．dx＝1lnaa2x2Cxa2x2ax66．dx＝a2x2Cx2a2x2a2x67．a(chǎn)2x2dx＝xa2x2a2arcsinxC22a68．(a2x2)3dx＝x(5a22x2)a2x23a4arcsinxC88a69．xa2x2dx＝1(a2x2)3C370．x2a2x2dx＝x(2x2a2)a2x2a4arcsinxC88a71．a(chǎn)2xx2dx＝a2x2alnaa2x2Cx72．a(chǎn)2x2a2x2arcsinxx2dx＝xCa（九）含有ax2bxc(a0)的積分73．dx＝1ln2axb2aax2bxcCax2bxca優(yōu)秀文案合用標(biāo)準(zhǔn)文檔74．a(chǎn)x2bxcdx＝2axbax2bxc4a4ac2b2bxcC8a3ln2axb2aax75．a(chǎn)x2xdx＝1ax2bxcbxcabln2ax2bxcC2b2aaxa376．dx＝1arcsin2axbCcbxax2ab24ac77．cbxax2dx＝2axbcbxax2b24acarcsin2axbC4a8a3b24ac78．xdx＝1cbxax2barcsin2axbCcbxax2a2a3b24ac（十）含有xa或(xa)(bx)的積分xb79．xadx＝(xb)xa(ba)ln(xaxb)Cxbxb80．xadx＝(xb)xa(ba)arcsinxaCbxbxbx81．dx＝2arcsinxaC(ab)(xa)(bbxx)82．(xa)(bx)dx＝2xab(xa)(bx)(ba)2arcsinxaC44bx(ab)（十一）含有三角函數(shù)的積分優(yōu)秀文案合用標(biāo)準(zhǔn)文檔83．sinxdx＝cosxC84．cosxdx＝sinxC85．tanxdx＝lncosxC86．cotxdx＝lnsinxC87．secxdx＝lntan(x)C＝lnsecxtanxC4288．cscxdx＝lntanxC＝lncscxcotxC289．sec2xdx＝tanxC90．csc2xdx＝cotxC91．secxtanxdx＝secxC92．cscxcotxdx＝cscxC93．94．95．96．97．98．99．

sin2xdx＝x1sin2xC24cos2xdx＝x1sin2xC24sinnxdx＝1sinn1xcosxn1sinn2xdxnncosnxdx＝1cosn1xsinxn1cosn2xdxnndx＝1cosxn2dxsinnxn1sinn1xn1sinn2xdx＝1sinxn2dxcosnx1cosn1xn1cosn2xncosmxsinnxdx＝1ncosm1xsinn1xm1cosm2xsinnxdxmmn＝1ncosm1xsinn1xn1cosmxsinn2xdxmmn優(yōu)秀文案合用標(biāo)準(zhǔn)文檔100．sinaxcosbxdx＝1cos(ab)x1cos(ab)xC2(ab)2(ab)101．sinaxsinbxdx＝1sin(ab)x1sin(ab)xC2(a2(ab)b)102．cosaxcosbxdx＝1sin(ab)x1sin(ab)xC2(a2(ab)b)dx2atanxb103．a(chǎn)＝a2b2arctana22C(a2b2)bsinxb2dx1atanxbb2a222104．＝ln2C(a)absinxb2a2atanxbb2a2b2105．dx＝2abarctan(abxC22abcosxababatan)(ab)b2dx1abtanxab106．＝ln2baC(a22)abcosxabbabtanxab2ba107．dxsin2x＝1arctan(btanx)Ca2cos2xb2aba108．dxsin2x＝1lnbtanxaCa2cos2xb22abbtanxa109．xsinaxdx＝11xcosaxC2sinaxaa122110．x2sinaxdx＝x2cosaxCaa2xsinax3cosaxa111．xcosaxdx＝12cosax1xsinaxCaa112．x2cosaxdx＝1x2sinax2xcosax2sinaxCaa2a0）a3（十二）含有反三角函數(shù)的積分（其中優(yōu)秀文案合用標(biāo)準(zhǔn)文檔113．a(chǎn)rcsinxdx＝xarcsinxa2x2Caa114．x＝x2a2xxa2x2Cxarcsindx(4)arcsin4a2a115．x2arcsinxdx＝x3arcsinx1(x22a2)a2x2Ca3a9116．a(chǎn)rccosxdx＝xarccosxa2x2Caa117．xarccosxdx＝(x2a2)arccosxxa2x2Ca24a4118．x2arccosxdx＝x3arccosx1(x22a2)a2x2Ca3a9119．a(chǎn)rctanxdx＝xarctanxaln(a2x2)Caa2120．xarctanxdx＝1(a2x2)arctanxaxCa2a2121．x2arctanxdx＝x3arctanxax2a3ln(a2x2)Ca3a66（十三）含有指數(shù)函數(shù)的積分122．a(chǎn)xdx＝1axClna123．eaxdx＝1eaxCa124．xeaxdx＝12(ax1)eaxCa125．xneaxdx＝1xneaxnxn1eaxdxaa126．xaxdx＝xax12axClna(lna)127．xnaxdx＝1xnaxnxn1axdxlna21lna128．eaxsinbxdx＝b2eax(asinbxbcosbx)Ca優(yōu)秀文案合用標(biāo)準(zhǔn)文檔129．eaxcosbxdx＝212eax(bsinbxacosbx)Cab130．eaxsinnbxdx＝212n2eaxsinn1bx(asinbxnbcosbx)abn(n1)b2axsinn2bxdxa2b2n2e131．eaxcosnbxdx＝a21axn1nbsinbx)b2n2ecosbx(acosbxn(n1)b2axcosn2bxdxa2b2n2e（十四）含有對數(shù)函數(shù)的積分132．lnxdx＝xlnxxC133．dx＝lnlnxCxlnx11134．xnlnxdx＝nxn1(lnx)C1n1135．(lnx)ndx＝x(lnx)nn1n(lnx)dx136．xm(lnx)ndx＝1xm1(lnx)nmnxm(lnx)n1dxm11（十五）含有雙曲函數(shù)的積分137．shxdx＝chxC138．chxdx＝shxC139．thxdx＝lnchxC140．sh2xdx＝x1sh2xC141．ch2xdx＝x214s