高等数学积分公式大全.docx

一）含有dxaxb的积分（a0)2.3.4.5.6.7.8.9.10.12.13.ax(ax1lnaaxb)dx=a(1)x1axbax(axb)1C(1)dx=4(axb।a-dxbdxx(axb)dxx2(axb)■dx2由47dxdxblnaxb)C11/-2(axaxb)2工当nbxb3(lna1g—(axaax2b(axb)b2Inaxaxb占)axb2blnaxbb2axb2x(axb)b(axb)含有vaxb的积分51n4a_bdx=—7(ax~b)33ax■,axbdxx2、-axbdx215a22axbdxaxb(3ax2b),(axb)3C105a3(15a2x212abx8b2).(axb)32,—2(ax2b)、axbC3adxU(3a2x24abx8b2)、、axbC15a15.dxx“axb16.dxx2..axb17.18.19.20.(四)22.23.24.25.In2一arctan、baxbbxaxb.dx=2Vaxb含有x2dx2a(x2C(b0)dxdx-2xi含有axb2….a2的积分=一arctan一axba2bC(b0)dxx*axbdxx%axbdxxvax2n3dx2、n22a)2(n1)a(x2xn1a)222、n12(n1)a(xa)2axdx2-axx2~ax2xaxLn2ab(a0)的积分14a小一arctan.xC、ab\bax'・b」ln2，ab>/axb~~b(b0)C(b0)-dxb-dxbdx'2——x(axb)dx12ai2ulnaxb12blnx2(ax2b)bxdx2axb2x2axdx2,axb27.-2.dx_aI-axb~32—T2ln2x3(ax2b)2b2x212bx228.dxx1dx(ax2b)22b(ax2b)2bax2b2一(五)含有axbxc(a0)的积分29.dx—2~~axbxc2.4acb2，2axbarctan「,4acb21ln2axbJb24acvb4ac2axbVb^4ac(b24ac)C(b24ac)30.-2dxaxbxcLn2a2ax,bdxbxc———22aaxbxc(六)含有&a2(a0)的积分dx.x2a2,xarsh一aC1=ln(xa2)C32.dxa2.x2a2.(x2a2)31x34.35.36.37.2dx^=dx2X3a)dxdx2\3a)2a—ln(x2x2a2)ln(x'x2a2)1lna~22xxaacxdxax39.了)C2_4"x~a_2dx=—4x_a2—in(xvx2240.(x2~a2)3dx=-(2x25a2)^x~0^83a4ln(x,x2~a^)C842.2-22,*x2xVxadx=-(2x82、2^22a)\xa43.~2.xa,-22—:——dx=Vxax\x2a2aln44.~2-xa,2——dxx~2xaln(x(七)含有病a2(a0)的积分45.dxx，x,xarch—C1=Ina46.dx.(x2a2)3xa2.x2a247.—x--dx22xa,x2a2C48.7r=x—dx=-^1==2■,(x2a2)3xa49.=改=xvx^~a2a222aIn250..(x2a2)3dx一 arccosLdx22x\xa53._2;-22.x2-2Ta,Vxadx=—yxa——lnx2254.~22-T,x22、-2xa)dx=-(2x5a)更多>