1、精品C感謝下載載(一)含有axb的積分（adxaxb1lnaxba(axb)dxxdx=axb2x-dx=axbdxx(axb)積分公0)1a(1)1,.(axba11/-2(ax1lnbax(axblnb)2b)axb)2b(ax1)2b)bInaxdxx2(ax b)ax b1a,axb0lnbxb27.x,2dx=(axb)-12(lnaax弋)axb2x(axb)2,1,dx=(axa2blnaxbb2axb)Cdxx(axb)2b(axb)5naxb(二)含有.axb的積分4bdx=J(axb)3axx/ax_bdx=-27(3ax2b)7(ax_b)15a2x2>/ax_bd

2、x=-(15a2x212abx8b2)7(axb)3105axdx="22(ax2b)/axbCaxb3a精品X2999'_,dx=z-(3ax4abx8b)vaxbC.axb15a3dxx、ax b(b(b0)0)dxx2 . ax bax b a dxbx 2b x、ax bC感謝下載載axb,小r,dxdx=2Jaxbb-xx%axb.axb,.axbadxdx=xx2x、axb（三）含有x2a2的積分dx1x19.-2=-arctan-Cxaaa2n 3-22(n 1)adx72、n 1(x a )dx_x,22、n=/2,22、n1(xa)2(n1)a(xa)dx1

3、,lxa3V=Wln|xa2（四）含有axb（a0）的積分dx-2ax b(b 0)C (b 0)xax2 b,1.dx=lnax2a2x,xbdxrdx=2.axbaaaxbdxx(ax2 b)In 2b2x2,ax bdx1adxx2(ax2b)bxbax2b2.dxaaxb13,2.-2-1n22x3(ax2b)2b2x22bx2dx22(ax2 b)2x1dx222b(ax2b)2bax2b2（五）含有axbxc（a0）的積分(六)dx2"ax bx c2xdx =ax bx c含有.x22 /a (a24ac=arctan b22ax b c 4ac b2(b2 4ac)2

4、a2ax b 、b2 4aci 2 uln ax bx0）的積分dx2,2a ax bx c2(b 4ac)dx2x a,x =arsh- aC1= 1n(x Jx2 a2) Cdx(x22 3a )xTx2"=dx =2 a,x2a2 C>xdx(x2a2)32x22x ax-22dx=Vxa2Tln(x22x.一(xa)x-x2=a*2ln(x.x2a2)22x a2a xa2)dx.(x2 a2)3dx= t(2x2 點(diǎn))”34-22_-aln(xxa)C82-22x_2xVxadx=-(2x84_n(xXVxadx =a2)C22xa“W_2:-dx=vxax22xaa

5、ln222a.xadx=ln(x含有vxa2(a0)的積分dx22xax_archC1=Inadx_x22322xa)axx,-2：22dx=Vxaxax2a2)x2a2精品感謝下載載23a)2x22xadx2-In2Indxxx=dx =23a )222a21=arccosa2.x a2a xdx2-In254 .5a2), x2In,22、3, . x a/(xa)dx=(2x8a2)3C222,x2xMxadx=(2x84-ln822xa22dx=yxaaaarccosx22xa.2dx=xInx，.x2a2含有a2(a0)的積分=arcsin-Cadx.(a2x2)3616263646

6、566676869707172一 a* 2 * * *(a2dx2 3x ),a2 x2a2=dx =2 x一 arcsin 一dx=dx = 2X3x ) a2 x2arcsin - Cax % a2 x2=1lnaa 、a2 x2dx22一 arcsin 一.ax(a2x2)3dx=護(hù)22x2x2)3C一aarcsin一222x2xvaxdx=(2x8a2)、,a2x2一arcsin一22ax1二2dx=vaxxa、a2x2aln,a2x2arcsin-Ca(九)含有.ax2bxc(a0)的積分dxax2bxc11aIn2axb2VaVax2bxc-axbx=2axb2=cdx='

7、Vaxbx4a.ax2bxdx=dxcbxax2&bxax2dx=Ix2dx=.cbxax2含有(x79.4acb2,八In2ax2VaVax2bxcC2a：ax2bxc12axb-arcsin:、ab4ac2axb2cbxax4a或(xa)(bb)80.81.b24ac.2axb-arcsinC8a34acx）的積分b)Fb.arcsin2、a32axb4ac(ba)ln(JxaJxb)xa八(ba)arcsin:Cbx=2arcsin后C(ab),(xa)(bx)dx2xab.(xa)(bx)（十一）含有三角函數(shù)的積分(ab)8384858687888990919293949596

8、979899sinxdx=cosxCcosxdx=sinxCtanxdx=lncosxCcotxdx=InsinxCx,.-secxdx=Intan(-)C=InsecxtanxC42x,.一cscxdx=Intan-C=IncscxcotxC22secxdx=tanxC2cscxdx=cotxCsecxtanxdx=secxCcscxcotxdx=cscxC一一2x1.sinxdx=-sin2xC242x1cosxdx=-sin2xC24n1n1sinxcosxn1cn2.sinxux一nnsinxuxcosnxdx=1n1.n1ncos2,xdxncosxsinxndx1cosxn2dxs

9、innxnn11sinxn1.n2sin1xdx1sinxn2dxcosnxn1n1cosxn1n2cosxmn1m1,n1m1m2.n,cosxsinxdxcosxsinxdx=cosxsinxmnmnm1ncosxsinm_n2cosxsinxdx精品含有反三角函數(shù)的積分（其中a 0）感謝下載載sinaxcosbxdx=2(ab)cos(ab)x2(ab)cos(ab)xCsinaxsinbxdx=2(ab)sin(ab)x2(ab)sin(ab)xCcosaxcosbxdx=2(ab)sin(ab)x2(ab)sin(ab)xdx2arctanabsinxatan-b2.a2b2C(a2

10、b2)dxabsinxln,b2a2*x22atanb.ba2(a2b2)dxabcosxdxabcosxdx22722acosxbsinxatan-2b；b2a2abarctan(abab,_x、tan-)ab2(a2b2)1CCabarctan(tanx)abadx11nbtanxa22.2.2acosxbsinxln2abbtanxa1xsinaxdx=sinax1-xcosaxCa2.12a2xsinaxdx=xcosax-yxsinaxC108.109.110.aa2cosaxa(a2b2).11.八xcosaxdx=cosax一xsinaxCaa2122“ccxcosaxdx=xs

11、inax2xcosaxaa2 .八3 sinaxC3a精品arcsinxdx=xarcsinVa2aa.x.，xa、xarcsindx=(一)arcsina24感謝下載載x2arcsinxdx=a3x一xarcsin一1/29(x2a2).a2arccosxdxax=xarccosaxarccosxdx=a2a、)arccos42xxarccosdx=a一arccos-1/29(x2a2).aarctan -dx = xarctan 一x2) Ca2ln(a2xarctanxdxja2a22x*x)arctan一a2，xx.xxarctan-dx=一arctan-3a/2一ln(a6x2)含有

12、指數(shù)函數(shù)的積分x1adx=lnaax1edx=eaxCaxCaax1/xedx=(axanax1naxxedx=xea_xxxxadx=alna1nxnxadx=xalnaax1)e1axedx2a(lna)Ina1axdx128.axe1/X/bcosbx)Csinbxdx22e(asinbxab129.axecosbxdx=-2eax(bsinbxa2b2acosbx)C130.axeQinbxdx=1eax_n1sinbx(asinbxnbcosbx)sinbxdx222eabnn(n1)b2222abn_ax_.n2esinbxdx131.axen.1accohvancos1bx(ac

13、osbxnbsinbx)COsbxdx222eabnn(n1)b2222abn_axn2ecosbxdx（十四）含有對數(shù)函數(shù)的積分132 .Inxdx=xlnxxC133 .dx=InInxCxlnx134 .xnlnxdx=xn1(lnx)Cn1n1n1135 .(lnx)ndx=x(lnx)nn(lnx)dxmn1m1nnmn1136 .x(lnx)dx=x(lnx)x(lnx)dxm1m1(十五)含有雙曲函數(shù)的積分137. .shxdx=chxC138. chxdx=shxC139. thxdx=lnchxC.2.x1一一140.shxdx=sh2xC242x1_141.chxdx=-sh2xC24（十六）定積分142 .cosnxdx=sinnxdx=0143 .cosmxsinnxdx=00,mn144 .cos