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__________________________________________________________________________________________________fu)duFu)C求g(x)dxf(x))'(x)dxf(x))d(x)fu)duFu)Cu(x)F(xCu(x)】g(x)dxf(x'(x)dxg(x)dxf(x))x)dxf(x))d(x)g(x)dxf(x))'(x)dxf(x)d(x)fu)u（3）作變量代換u(x)g(x)dxfu)duFu)Cf(x))'(x)dxf(x))d(x)fu)uFu)Cg(x)dxu(x)xf(x))'(x)dxf(x))d(x)fu)duFu)CF(xCg(x)dxu(x)1(5x7)9dx(5x7)9dx(5x7)d(5x7)9515(5x7)d(5x7)91111(5x7)9d(5x7)(5xC(5xC5510501(5x7)'5,d(5x7)5dx,dxd(5x7)5lnx1dxlnxxxdxlnxdlnx11lnxdlnx(lnx)2Cx)2C22111

(lnx)',d(lnx)dx,dxd(lnx)

xxxtanxdxsinxdxsinxdxdcosxdcosxcosxxcosxcosxdcosxln|cosx|Cln|x|Cx精品資料__________________________________________________________________________________________________xx,dx)xdx,dx)cotxdxcosxcosxdxdsinxdxsinxsinxsinxdsinxsinxln|sinx|Cln|sinx|Cxx,dx)xdx,dx)111

dxdxd(ax)

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axd(ax)ln|ax|Cln|ax|C(ax1,d(ax)dx,d(ax)111dxdxxaxaxad(xa)1xad(xa)ln|xa|Cln|xa|C(xa1,d(xa)dx,d(xa)11111111x2a2x2a22axaxa2axaxa11xa|xa||xa|C2a2axaCxxx)sec2xxxxxxxdtanxsecx)dtanxsecx)ln|secxtanxsecxtanxxtanx|Csecxdx1cosxcosxdxdsinxdxdxcosxcos2xcos2x1sin2xdx1111x111xdsinxCC1x2x1x12x121sinx2xxx)csc2xxxxxxxd(cotxcscx)dcscxcotx)ln|csccscxcotxcscxxxcotx|Cxxx)csc2xxxxxxx精品資料__________________________________________________________________________________________________d(cotxcscx)dcscxcotx)ln|cscxcotx|Cxcotxcscxx11x21x2xC1a2x2a2x2x2a1axdax21axdax21axaC1dxdx1x21x2arctanxCxxdd11a1a1xaxaxxaxaxaa2222222a2111aaaCa0）sin3xcos5xdxsin2xcos5xsinsin2xcos5xdxx)xdx257cos8xcos6xxx)dxC586sin3xcos5xdxsin3xcos4xsin3xcos4xdsinx4x6x8xxx)dxxxx)dxC322357438dx1111dxdlnxxlnxxxlnxlnxdxlnxCdx11111dxdxdlnxCxlnxlnxxlnxlnxlnx2222222d(x2)x2Cx2x2x2x2x2x21(x)42424222121dx21d(x2)x2x52x2x52x2x524(x)42424222x21d21d(x21)11x21arctan()8x14x14222221122C精品資料__________________________________________________________________________________________________sinx11dxsinxdx2sinxdx2sinxx2xxdx2sinxdx2cosxC2cosxCedx2x1211ed2xed2xeC2x2x2x22xxxdx3333xdsinx4x4C11(2x100dx(2x5)dx(2x5)d(2x5)(2x5)d(2x5)221111(2x100d(2x5)(2xC(2xC221012022xsinxdxsinxxdx2111sinxdxsinxdxcosxC22222222xx1x(1x)1dxx1x1xx1x1xdx1lnxdlnx11lnxdlnx11lnxdlnx)1lnxdlnx)231lnx)2lnx)2C3ex1eedxedxeCxxxx1x1x22x1x211x2121x22121x2dx2)121x2dx2)1x2Cxcos3x1cos3xsin1cos3xdxcos32dcosx2cos12xC精品資料__________________________________________________________________________________________________ex111eded(2e)ln(2e)Cxxxx2e2e2e2exxxxln2x1ln3xxxdxxdxC222xx3dx12xx2dx2x)2dx)2(1x)2dx)(2)2x)21xarcsinC211d(x)d(x)dxdx221717xx2(172x)2(x)2(x)2()224242211d(x2)2x222x1Carctan177777()()x222Cxxa22xb2cos2x，a2b2(asinxbcosx)'a2sinxcosxb2cosx(sinx)2(ab)sinxcosx22222222d(asinxbcosx)2(ab)sinxcosxdx222222x12(ab)22d(axbx)2222sinxcosxa2sin2xb2cos2xdx1sinxcosxdxd(a2sin2xb2cos2x)asinxbcosxab2asinxbcosx22222222221d(a2sin2xb2cos2x)1asinxbcosxC2222ab2asinxbcosxab22222222精品資料__________________________________________________________________________________________________ft)dtFt)C求g(x)dxgt))dt)gtt)dtxt)ft)dtFt)CF1(x))Ct1(x)】xsintsintdx令xt2xtttx2變量還原tCxCtx111t1dx1令xt21xxt1t1t1t1t222xln|1x|Ctln|1t|C變量還原tx111t11dxdt2(t1)11+xt21xtx(t1)ttt2變量還原2tln|t|C21xln|1x|Ctx111343令xt1xdxtdtttt343324x(t1)txt31)432343(14x73(14x4tt7463C12tt)dt12C747434tx1111令xttdt22xx)xttt)t(1t)1t22222arctantC2arctanxCtx精品資料__________________________________________________________________________________________________1111111xetdtdt1ex1t1tttt)t1txttexln|t|ln|1t|ClnClnC1t1exxtedx11t216令xtdttdt6dt61dt65x)xxttttt1t1t2323223

6tt)C6x6x)C6txx,xtnxkmk為,nt23t23x2tt|1t|Cxt32t2x233(x2)2變量還原x2ln|1x2|C3362txx令tt211x2dtt2ln|t1|ln|t1|Cx21t12xxx2t11x1x1x22ln|1|ln|1|Cxxxxtxaxbn或axbntcxddxxx2)811d12t81令tttxttt1642111111t1tx22t11t8t2t8t2t7t5t311111tarctantCarctanC7537x5x3xxx7531

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x精品資料__________________________________________________________________________________________________111ln1ln11lnxt11lntt1令txd1111x(ln)xxtt22221tlnlntttt111(1lnt)dtd(1tlnt)C1tlnt1tlnt221tlnt變量還原1tx1xCC11xlnx1lnxxtt11x1sinx1tt1t令t222dxd2arctansin(1cos)t1t22t1t21t2xt(1)(1)1t1t1t1t222211t21t2dttln|t|C

2t42xtan2x1x2tanln|tan|變量還原C14222tx令xasint|axdx222a2a2sin2tdasinta2cos2tdttxadxa2x2令xasint|2xtadasinta2a2sin2txdttCarcsinCxataa21cos2ta2a2sintdtcos2t)dttC2222a2x1變量還原arcsinxa2x2Cx2a2tadx222dat令xat|22tan2txtarctanasectdtln|sectt|Cx22ln|xaatarctana|Cln|x22|C精品資料__________________________________________________________________________________________________a2(xa2x2)'2a2x2ax22(xa2x2)'dx2a2xdx2a2a2x2dx11ax(xax)'a222222a2

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