高等数学常用积分公式查询表.docx

导数公式:(tgx)sec2 x(ctgx)cscIn2a i 2 2 一ln(x x a ) C22 j a . .■ 2 2 c——ln x \ x a C2 a . x —arcsin — C 2 a x(secx) secx tgx (cscx)cscx ctgx(ax)axlnaZl 、1(logax) xlna(arcsin x) ,1 x21(arccosx) 2,1 x1(arctgx) 21 x,、1(arcctgx) 21 xdx22sec xdxtgx Ccos xdx2. 2csc xdxctgx Csin x基本积分表：tgxdx In cosx C ctgxdx In sin x C secxdx In secx tgx Cdxcscxdx In cscx ctgx Cdx1x12一 arctg一 Ca xaadx1,lxa 「w—2 —lnCx a 2a |x a1 , a x—ln2a a xsecx tgxdx secx Ccscx ctgxdx cscx Cxx a axdx ——Cln ashxdx chx Cchxdx shx Cdx.x _arcsin- Cadxln( x,x2a2)C.x2 a222I n sinn xdxcosn xdx0022 , x 22x a dx — x a 222x22.x a dx — x a2da2 x2dx x Ta2""x22三角函数的有理式积分:一.一 2u —1sin x 2, cosx -1 u12幺2， udx -12duu2(一)含有ax b的积分(a0)dxax b a1ln ax2.(ax b) dX1 a(一 (ax1)b)1)3.—x-dx ax b1 ,.— (ax b ablnaxb)4.2x1ax b1 1/—2(axb)22b(axb),2 .b In ax5.dxx(ax b)1ln bax6.dxx2(ax b)7.x .2dx(ax b)8.2-dx9.dx(二)10.12.13.ax b1 a । ax b -—二lnCbxb2工(In ax a1 , 二 (axa2x(ax b) b(ax b)含有vOxb的积分弋)ax b2bln ax b4~bdx= —7(ax~b)33ax.ax bdxx2 \ ax bdx215a22ax bb2axb)(3ax 2b) ,(ax b)3 C105a3(15a2x2 12abx 8b2)、.,(ax b)3 Cxdx = ~^2 (ax 2bh/ax~b Cax b 3a14.2一x一.ax b-^-3 (3ax2 4abx 8b2). ax 15a（四）含有ax b（a 0）的积分15.dxx . ax b16.dxx2 . ax b17..ax b.dx18.而 Vax~b VbL arctan ,bbx2 . ax bax bax b2bC (bC (bdxdxdx0)0)20.dx(x22、n 2 2a ) 2(n 1)a (x2、n 1a )2n 32(n 1)a2dxT-2 2xn 1(x a )x % ax（三）含有x2 a2的积分dx1 x19.w2= 一 arctan —Cx aa adx~2 x i2a22.dx2- ax1 1 aarctan, x C,ab 1 b、ax 、一 b(b 0)1—ln2J ab 5/ax b~bC (b 0)x aln x a24.2x , x b dx2 .dx = - - 2 .ax b a a ax b25.dx 1 x 2 = - ln —2 x(ax b) 2b ax b26.dx 1 a dx x2(ax2 b) bx b ax2 b27.2 .dx a , ax b = In 3/2 2 1n 2x (ax b) 2b x28.dx x 1 dx(ax2 b)2 2b(ax2 b) 2b ax2 b2(五)含有ax bx c (a 0)的积分29.dxax bx c2 , 2ax b -/ 2 arctan / 2二 C4ac b . 4ac b1b2 4ac2ax b yb24ac ln2ax b 、. b2 4ac(b2 4ac)2C (b2 4ac)30.—2—x dxax bx cLn ax 2abx cdx2 ,2a ax bx c(六)含有&a7 (a 0)的积分x.22 一arsh- C1 = ln(x vx a ) C a32.dx x.(x2 a2)3 a2 x2 a233 -二 2 dx =& a2C，x a34.XdY=1/ 22X322.(x a )x a35.2、,x2 a2)x . x -# dx = — vx,x2 a2236.2 x-—27 dx x a )—x——ln(x22'\ x a..x2 a2)37.dx 1 ,x?xi=a2^n、.x2 a2 a C38.dxJx2 a2x2 , x2 a2 a2x39.：=22 , x .—22vx a dx = ~\jxa22 aln( x2、x2 a2)40.3 4 2 2.八a ln( x 、. x a ) C8；~2273 .x 22. ~7(x a ) dx = -(2 x 5a )vx8xvx^~a2dx=- 3a2)3 C42.x27xTVdxW(2x2a2) , x2a24—ln( x , x2 a2)C843.22、x a-22—:-dx = yx ax22,.x a a a In-x44.22x a .2—dxx22x a22、ln( x \ x a )(七)含有Vx2a7 (a 0)的积分45._dx_ xx2=a2" xarch) aC1 = In xJx2 a247.r^x~~； dx = 4x2 a2 C22、x a48.==X dx = -=J==2 C(x上 dx 2 \3 a2)x a )x a49.=dx= v?~a7 a222 aIn250.2ln、x a=-arccosLdx~22x \ x a52.dxvx2 a2x2 , x2 a2a2-53.