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1、常-用-积-分-公-式常用积分公式（一）含有 axb 的积分 ( a 0 )dx1 ln ax b C1 axb a( ax1(ax b) 1Cb) dx（1）2 a( 1)xdx12 ( ax b b ln ax b ) C3 axb ax211b)22b(ax b) b2ln ax b Cbdx a3(ax4 ax2dx1 ln axbC5 x( ax b) bxdx1a2 ln axbC2(ax b) 6 xbxbxx2dx1(ln ax bb) C7 (ax b) a2axbx22dx1b2(ax b 2b ln ax b) C8 (ax b) a3axbdxb)2112 ln axb
2、C9 x( ax b(ax b)bx（二）含有axb 的积分102(ax b)3Cax bdx 3a2311 x ax bdx 15a2(3ax 2b) (ax b)Cx2 ax bdx23 (15a2 x212abx 8b2 ) ( ax b)3C12 105axdx2(ax 2b) ax b C13 ax b 3a2x2dx22 2214 axb 15a3(3a x4abx 8b ) ax b C1axbbC(b0)lnaxbbbdx2arctanaxbC(b0)15 x ax b bbdxax badx16 x2 axb bx2bx ax bax bdx2 ax bdx17bxx ax
3、baxbdxax badx182x2x ax bx（三）含有 x2a 2 的积分dxa21 arctan xC19 x2= aadxx2n3dx20 ( x2a2 ) n= 2( n1)a2 (x2a2 ) n 12(n1)a2( x2a2 )n 1dx1xa21 x2lnCa2= 2axa（四）含有 ax 2b(a0) 的积分1arctana xC(b0)abbdx1lnaxbC(b0)b 222 ax 2abaxbxbdx1223 ax2 2aln axb Cx2dxx bdx24 ax2b a a ax2bdx1 lnx2C25 x(ax 2b) 2bax2bdx1 adx26 x2 (
4、ax2b) bx b ax 2bdxalnax2b1C3(ax2x227 xb) 2b22bx2dxx1dx28 ( ax2b) 2 2b(ax2b)2bax2b（五）含有 ax 2bxc (a0) 的积分2b2arctan2axbC(b24ac)4ac4acb2dx12axbb24ac24ac)b24aclnbb2C(b29 ax2bx c 2ax4ac30 ax 2xdx1 ln ax2bx cbdxbx c 2a2a ax2bx c（六）含有x2a2 ( a0) 的积分dx arshxC1 ln( xx2a 2 ) C31x2a2adxxC( x2a2 ) 3 a 2 x232a2xdx
5、33x2a2x2a2Cxdx1a2C( x2a2 )3x234x2dxx22 a22235x2a2 2xa2ln( xxa ) Cx2dxx22( x2a2 ) 3x2a2ln( xxa ) C36dx1x2a 2a37 x x2lnCa2 axdxx2a238 x2 x2a2a2 xCx 2xx2a2a2x2a2) Ca2 dxln( x39 22223x22223422(2 x5a ) xaaln( xxa ) C40( xa ) dx 88221223( xa )C41 x xa dx 3222x2222 a422(2 xa ) xaln( xxa ) C42 xxa dx 88x2a2
6、 dxx2a2a lnx2a2aC43xx44x2a2dxx2a 2ln( xx2a2 ) Cx2x22（七）含有xa( a0) 的积分dxxx45 x2a2 xarch aC1=ln xx2a2CdxxC46( x2a 2 )3 a2 x2a2xdx47x2a2x2a 2Cxdx122 3x2C48( xa )a2x2xa22 dx49 x2x2a2ln xx2a2Ca 22x2dxx22( x2a 2 )3x2a2ln xx aC50dx1aarccosC51 x x2a 2 axdxx2a252 x2 x2a2a2 xCx2a2 dxxx2a2a2 ln xx2a 2C53 22x(2 x25a2) x2a234ln xx2a2C( x2a2)3dx 8a854221223( xa )C55 x xa dx 3222x2222a422(2 xa ) xaln xx aC56 xxa dx 88x2a222adxxaa arccosC57xxx2a2x2a2x2a2C58x2dxln xx（八）含有a2x2 ( a0) 的积分dxarcsin xC2x259 aadxxC60(a2x 2 )3 a 2 a2x2xdx61a2x2a2x2Cx
