高等数学常用积分公式查询表.docx

导数公式:(tgx)(ctgx)(secx)(cscx)(ax)2secx2cscx(arcsinx)根本积分表secxtgxcscxctgxIna(arccosx)(arctgx)(lOgax)xlna(arcctgx)1Tx212.1x12x11x2tgxdxIncosxctgxdxInsinxsecxdxInsecxdx2-cosxdx2sinxsecxdxcsc2xdxcscxdxIncscxctgxCsecxtgxdxsecxtgxCctgxCdx~22axcscxctgxdxcscxCdx~~22axdx2aax1,xc一arctg一Cdx22xaaxdxshxdxchxdxInachxshx,a2x2___xarcsin—adxx2一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) dxx 1ax bax b(axb), 1， ，dx = —(ax b' a2—x-dxax b1 1 /3 2(axblnb)2axb) C2b(ax b)b2 In axdxx(ax b)dxx2(ax b)x(ax b)2dx 2dx(ax b)dxax1lnax bax bbx工(In a1 , (axaax七)ax b2bln ax b昌) ax b2x(ax b) b(ax b)1 । ax L—7 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.dxaxbdxx।axbdxx2.axb2,—7(ax2b),axbC3a2(3a2x24abx8b2).ax15a2(b(baxbbxa2bdxx.axb0)0)axb,-dx=2vaxbaxbaxbdxx,axbdxx.ax含有x2dx~22xadx(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-Larctanab—1—ln(b0)2yabTaxsA-bC(b0)23.x2-ax-dxb12alnax2b24.2xax-dxb25.dx/2x(axb)26.dx2,2—■x(axb)27.dx2x(axb)28.dx22(axb)〔五〕含有ax2bx29.dx2_axbxc30.〔六〕32.33.Ln2b1bx2axdx—2~~~axb2x2ax-^2In2b2dxax2.axb2x_22b(axb)12bc(a0)的积分dx2--axb2.2axb八arctanC4acb24acb21lnb24ac,1.dx=一Inaxbxc2a含有.x2dx~22xadx2a(a0)的积分2axb、b24ac2axbx4ac(b2C(b24ac)4ac).x一arsh—Ci=ln(xC.(x^Vb2ax2a2)dx2axbxc34._^dx='(x2a2)3.x2a35.=dx=—'7x2~a^a2227ln(x36.2dx22\3xa)ln(x厂a2)37.dxx\x2a2a1x2a2a—In：C38.dx2~2xxa~~22,xa2ax39.—22,x—22vxadx=vxa22a।/—ln(x2a2)40.7(xa2)3dx=x(2x2，8x7x2~a2dx=-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=249.2X「22a.一,xa—ln2222X3a)x.xdx=一22\32xa),xAndxx、x2dx2~~22x.xa一arccos—22xa2ax~2,x222Vxadx=-Mxa2；~2273」x27(xa)dx=-(2x82-22X2xvxadx=(2x822xa2~~"Jdx=vxax22xa」2——dxx2aIn25a222alna2)3Ca2).x2a2aaarccosxln含有da2x2(a0)的积分dXarcsinXCa4—ln860.dxx(a2x2)3a2a2x261•—Fdx=荷x2C、ax62.(a2x2)3dx,a263.a2=dx2x一arcsin一64.^=dx23x)a2一一xarcsin一a65.dxx、.a2x21lnaa66.dxx2a267.2 , x dx一arcsin一68.7-22~3,x2V(ax)dx=-(5a2x2)a269.xa2x2dx[.(a23x2)3C70.2--22.x，axdxx2(2x8a2)'a222,ax,dxxaln72.34.aarcsin8一arcsin一、a2x2~~22-22ax,ax.x八2—dx=arcsin—Cxxa〔九〕含有4ax2bxc(a0)的积分73.dx74..ax2bxcIn2axb2aax2bxcax2bxcdx2axb—2-.\axbx4a2>/aVax2bxcC75.x.——dxax \ a3 一 b2 4acbxc1gx2bxca76.dx.cbxax277.,cbxax2dx―b=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=Intan—C=IncscxcotxC289. secxdx=tanxC290. cscxdx=cotxC91. secxtanxdx=secxC92。