文档介绍：SOUTHEASTUNIVER()dx=d(ax+b)(2)xdx=d(x2);(3)dx=d(Inx)(4)-dx=-d(-)(5)dx=2l(x)(6)dx=d(arctanx)1+Xdx=d(arcsinx)(8)edx=d(e1-x0)sinrdr=-d(cosr);(10)cosxdr=d(sinr)(11)secfxdx=d(tanx);(12)csctxdx=-d(cotx);(13)secrtanxdx=d(secr);(14)cscrcotxdx=-d(cscr)SOUTHEASTUNIVERSITYdx例4(2)(a>0)去根号x+1dx分母不能因式分解x2+x+1一般做法:消x,把它写成分母的导数,再凑x+1(4)dx分母可因式分解x2+x-2法一:同(3)法二:化为部分分式之和差SOUTHEASTUNIVERSITYx+1例4(52x+1x2+x+1x2+x-2d(cosx)(6)tanxdx-oscosd同理∫cotxdx=lnsinx+C思考:」tanfxdxtandotantra(7)cosxdx=SOUTHEASTUNIVERSITYsInrtanrdr例4-(8)「osc法secrardrcosrcosrd(sinx)十d(sinx)1-sin2x2(1+sinx1-sinx=L工法二secx(secx+tanr)secraxx+tanxInx+tanx+CSOUTHEASTUNIVERSITY例5(1)「a2-x2dx(a>0)解:令x=asint元<t<22),则dvc原式=∫a-a2sin't'acostdt=a∫ost:st暂时借用TE到时还原一粗制滥造扣分SOUTHEASTUNIVERSITY例5(1)「a2-x2dx(a>0)去根号解:令x=asinx(-x<t<x),则xcas4r-x-dx2(t-+sintoost)+CSOUTHEASTUNIVERSITYx-10例6(1)去根号x2+1解:设x=tanu(0<<),则d=sumkxx-2d(3)√x2+1√x2--10]secuduVx+SOUTHEASTUNIVERSITY所用的代换称为三角函数代换去根号()a2-x2时,令x=asin(2)Vx2+a2时,令x=catan;vr-a时,令r=asecSOUTHEASTUNIVERSITYdx例7去根号xx2-1九种解法法一:(三角代换法)令x=secu,0<t<元2则dx=secuduReNuG=ai=+c=os-+CSOUTHEASTUNIVERSITYdx例7去根号rvr1法一:(三角代换法)法二:(根式代换法)令√x2-1=t,则x2=1xdr=tdtdxxdrtdtr√x2-1(1+t)tatarot