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1、导数公式:(tgx)(ctgx)(secx)(cscx)(ax)2secx2cscx(arcsinx)根本积分表secxtgxcscxctgxIna(arccosx)(arctgx)(lOgax)xlna(arcctgx)1Tx212.1x12x11x2tgxdxIncosxctgxdxInsinxsecxdxInsecxdx2-cosxdx2sinxsecxdxcsc2xdxcscxdxIncscxctgxCsecxtgxdxsecxtgxCctgxCdx22axcscxctgxdxcscxCdx22axdx2aax1,xc一arctg一Cdx22xaaxdxshxdxchxdxInachx
2、shx,a2x2_xarcsinadxx2一ln(x.x2a2)Ca2Insinnxdx0ncos0xdx,x2a2dxxx2a2222,xadxa2x2dx2ln(xx2a2)C2.a.一Inx22a.x_arcsin-C三角函数的有理式积分:sin x - 12u2 u,cosx2J2， udx -12duu2一含有dxaxb的积分（a0)2.3.4.5.6.7.8.9.ax(ax-ln b ab) dxx1ax bax b(axb),1，dx = (ax b a2x-dxax b1 1 /3 2(axblnb)2axb) C2b(ax b)b2 In axdxx(ax b)dxx2(ax
3、 b)x(ax b)2dx2dx(ax b)dxax1lnax bax bbx工(In a1 , (axaax七)ax b2bln ax b昌) ax b2x(ax b) b(ax b)1 ax L7 In b2ax二含有Jaxb的积分10. Waxbdx=T(ax_b)3C3a22311. xVaxbdx=2(3ax2b)J(axb)C15a12. x2Vaxbdx=-3(15a2x212abx8b2)J(axb)3C105a314.15.16.17.18.三19.20.四22.13.2x.dxaxbdxxaxbdxx2.axb2,7(ax2b),axbC3a2(3a2x24abx8b2).
4、ax15a2(b(baxbbxa2bdxx.axb0)0)axb,-dx=2vaxbaxbaxbdxx,axbdxx.ax含有x2dx22xadx(x2dx2xi含有2，a的积分=arctan一2、n22a)2(n1)a(x2、n1a)2n32(n1)a2dx-22xn1(xa)12axalnIxa2axb(a0)的积分dx2axb-Larctanab1ln(b0)2yabTaxsA-bC(b0)23.x2-ax-dxb12alnax2b24.2xax-dxb25.dx/2x(axb)26.dx2,2x(axb)27.dx2x(axb)28.dx22(axb)五含有ax2bx29.dx2_ax
5、bxc30.六32.33.Ln2b1bx2axdx2axb2x2ax-2In2b2dxax2.axb2x_22b(axb)12bc(a0)的积分dx2-axb2.2axb八arctanC4acb24acb21lnb24ac,1.dx=一Inaxbxc2a含有.x2dx22xadx2a(a0)的积分2axb、b24ac2axbx4ac(b2C(b24ac)4ac).x一arshCi=ln(xC.(xVb2ax2a2)dx2axbxc34._dx=(x2a2)3.x2a35.=dx=7x2aa2227ln(x36.2dx223xa)ln(x厂a2)37.dxxx2a2a1x2a2aIn：C38.d
6、x22xxa22,xa2ax39.22,x22vxadx=vxa22a/ln(x2a2)40.7(xa2)3dx=x(2x2，8x7x2a2dx=-J(x235a2)-x2a2)3C42.2-2-2.x2xVxadx=(2x843.22xa-22:dx=Vxax44.ln(x45.46.),x2a222,xaalntv含有Jx2a2(a0)的积分dxxx2a2xar2Ci=lna3a4ln(x.x2a2)C84,n(x.X2a2)C、.x2a2)dx(x2a2)3x2-22axa47.a2C48.50.52.53.54.55.56.57.58.59.dx=249.2X22a.一,xaln222
7、2X3a)x.xdx=一2232xa),xAndxx、x2dx222x.xa一arccos22xa2ax2,x222Vxadx=-Mxa2；2273x27(xa)dx=-(2x82-22X2xvxadx=(2x822xa2Jdx=vxax22xa2dxx2aIn25a222alna2)3Ca2).x2a2aaarccosxln含有da2x2(a0)的积分dXarcsinXCa4ln860.dxx(a2x2)3a2a2x261Fdx=荷x2C、ax62.(a2x2)3dx,a263.a2=dx2x一arcsin一64.=dx23x)a2一一xarcsin一a65.dxx、.a2x21lnaa66
8、.dxx2a267.2 , x dx一arcsin一68.7-223,x2V(ax)dx=-(5a2x2)a269.xa2x2dx.(a23x2)3C70.2-22.x，axdxx2(2x8a2)a222,ax,dxxaln72.34.aarcsin8一arcsin一、a2x222-22ax,ax.x八2dx=arcsinCxxa九含有4ax2bxc(a0)的积分73.dx74.ax2bxcIn2axb2aax2bxcax2bxcdx2axb2-.axbx4a2/aVax2bxcC75.x.dxax a3一 b2 4acbxc1gx2bxca76.dx.cbxax277.,cbxax2dxb=
9、ln2axba31arcsinbxcC2axb.b24ac2axb;2cbxax4ab24ac_arcsin8a32axbb24ac78.x-dx .c bx ax2b.2axb-一arcsinC含有或.(xa)(bx）的积分79.府dx二(xb)axb(ba)ln(JxaJxb)80.后dx=(xb)，xa，bx(ba)arcsindx.(xa)(bx)2arcsin府C(ab)/、小j2xab(ba).xa-82. ，(xa)(bx)dx=V(xa)(bx)-arcsinJC44bx(ab)十一含有三角函数的积分83. sinxdx=cosxC84. cosxdx=sinxC85. tanxdx=IncosxC86. cotxdx=InsinxCC = In secx tanx，x、87.secxdx=Intan(-)42,.x_.-88. cscxdx=IntanC=IncscxcotxC289. secxdx=tanxC290. cscxdx=cotxC91. secxtanxdx=secxC92
