高等数学积分公式大全1.pdf
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1、常常 用用 积积 分分 公公 式式一含有一含有axb的积分的积分a 01dx1ln ax b Cax ba1(ax b)1C 1a(1)2(ax b)dx3x1dx2(ax bbln ax b)Cax bax21 1dx3(ax b)22b(ax b)b2ln ax bC4a2ax b5671ax bdxClnbxx(ax b)1aax bdxlnC22bxbxx(ax b)x1bdx(ln ax b)C(ax b)2a2ax bx21b2dx3(ax b2bln ax b)C82(ax b)aax b911ax bdxlnCb(ax b)b2xx(ax b)2二含有二含有ax b的积分的积分
2、2(ax b)3C3a2311x ax bdx(3ax 2b)(ax b)C215a2(15a2x212abx 8b2)(ax b)3C12x2ax bdx3105a10ax bdx1314x2dx2(ax 2b)ax b C3aax bx22dx(3a2x24abx 8b2)ax b C315aax bdx15x ax b1lnbax b bC(b 0)ax b b2ax barctanC(b 0)bb161718x2dxax badxbx2bx ax bax bax bdxdx2 ax b bxx ax bax bax badxdx2xx2x ax b三含有三含有x2 a2的积分的积分19
3、2021dx1x=arctanCx2a2aadxx2n 3dx=(x2 a2)n2(n 1)a2(x2a2)n12(n 1)a2(x2 a2)n11x adxlnC=22x a2ax a四含有四含有ax2b(a 0)的积分的积分1arctandxab222ax b1ln2 abax Cb(b 0)ax bC(b 0)ax b23x12dxln ax b C2ax b2ax2xbdx242dx2ax baaax bdx1x2C25ln2x(ax2b)2bax b26dx1adxx2(ax2b)bxbax2b27dxaax2b1x3(ax2b)2b2lnx22bx2C28dxx1dx(ax2b)2
4、2b(ax2b)2bax2b五含有五含有ax2bx c(a 0)的积分的积分22ax 29dx4ac b2arctanb4ac b2Cax2bx c12ax bb24acb24acln2ax bb24acC30 x1bdxax2bx cdx2aln ax2bx c 2aax2bx c六含有六含有x2a2(a 0)的积分的积分31dxxx2 a2arshaC1ln(x x2a2)C32dx(x2a2)3xa2x2a2C33xx2 a2dxx2a2C34x(x2a2)3dx1x2 a2C35x2xx2a2dx2x2 a a222ln(x x2 a2)C36x2(x2a2)3dxxx2 a2ln(x
5、 x2 a2)Cdx1x2a237ax x2 a2alnxC38dxx2 a2x2x2 a2a2xC39x2a2dxx2x2 a2a22ln(x x2 a2)C(b2 4ac)(b2 4ac)40(x2a2)3dx(2x25a2)x2a2a4ln(x x2a2)C41x x2a2dx42x4344222x8381(x2a2)3C3xa42222x a dx(2x a)x a ln(x x2a2)C88x2a2x2a2a22dxx a alnCxxx2 a2x2 a222dxln(x x a)C2xx七含有七含有x2a2(a 0)的积分的积分454647484950515253dxx2a2xxa
6、rchC1=ln x x2a2Cxaxa2dx(x a)xx2a2223x a22Cdxx2a2Cx(x a)22 3dx1x a22Cx2a22x a ln x x2a2Cdx22x2a2x2x2(x2a2)3dxx x2a2dx1axx2a2ln x x2a2CarccosaCxx22x2a2C222a xx adxx2a22x a ln x x2a2Cx a dx22254(x2a2)3dx(2x25a2)x2a2a4ln x x2a2Cx83855x x2a2dx56x57582221(x2a2)3C3xa42222x a dx(2x a)x a ln x x2a2C88ax2a2dx
7、x2a2aarccosCxxx2a2x2a222dxln x x aC2xx八含有八含有a2 x2(a 0)的积分的积分596061626364dxa2 x2arcsinC3xa2xadx(a x)xa2 x222a x22Cdx a2 x2Cx(a x)22 3dx1a x22Cx2a2x2a x arcsinCdx22aa2 x2x2x2(a2 x2)3dxdxxa2 x2arcsinxCa1a a2 x2C65ln22axx a x6667x22a2 x2C222a xa xdxx2a2x2a x arcsinCa x dx22a2x8169x a2 x2dx(a2 x2)3C368(a
8、2 x2)3dx(5a22x2)a2 x2a4arcsinC38xa70 x71722xa4x2222a x dx(2x a)a x arcsinC88a22a2 x2a a2 x222dxa x alnCxxa2 x2a2 x2xdxarcsinCx2xa九含有九含有ax2bxc(a 0)的积分的积分73dxax2bx c1ln 2ax b2 aax2bx c Ca74ax2bx cdx75767778xax2bx cdxc bx ax222ax bax2bx c4a1ax2bx ca12ax barcsinC2ab 4acdx2ax bb24ac2ax b2c bx ax dxcbx ax
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