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1(1)xadx=xa+1a+1+C(a-1)(2)1xdx=ln|x|+C(3)axdx=axlna+C(4)sinxdx=-cosx+C(5)cosxdx=sinx+C(6)tanxdx=-ln|cosx|+C(7)cotxdx=ln|sinx|+C(8)secxdx=ln|secx+tanx|+C(9)cscxdx=ln|cscx-cotx|+C(10)sec2xdx=tanx+C(11)csc2xdx=-cotx+C(12)dx1+x2=arctanx+C(13)dxx2+a2=1aarctanxa+C(14)dxx2-a2=12aln|a-xa+x|+C(15)dxa2-x2=12aln|a+xa-x|+C(16)????1-??2=arcsin??+??(17)??????2-??2=arcsin????+??(18)??????2??2=ln|??+??2??2|+??(19)a2-x2dx=x2a2-x2+a22arcsinxa+C(20)x2a2dx=x2x2a2a22ln|??+??2??2|+??(1)????=??????????????(166)????=-cos??????????-1????+??-1??????-2()????nD1=sinxdx=-cosx+CnD2=sin2xdx=x2-sin2x4+C(2)????=????(??2+??2)??(173)????+1=12????2??(??2+??2)??+2??-12????2??????????1=dxx2+a2=1aarctanxa+C2()()1x+x-x2dxx+x-x2dx=-12(-2x+1)+12+x-x2dx=-12d(5+x-x2)+x-x2+121+x-x2dx=-5+x-x2+12dx(212)2-(x-12)2=-5+x-x2+12arcsin(2x-121)+C2x3x4+x2+1dx1x3x4+x2+1dx=14(4x3+2x)-12xx4+x2+1dx=14d(x4+x2+1)x4+x2+1-14d(x2+12)(x2+12)2+(32)23dx1+sin2xdxcos2x+2sin2x=1cos2xdx1+2tan2x=d(tanx)1+2tan2x3=12d(tanx)(22)2+tan2x=22arctan(tanx)+C4x3-x3dx=x32x(a32)2-(x32)2d(x32)=231(a32)2-(x32)2d(x32)512x+3dx=12x1+32xdx32x-3ln212x6x1-xcotxdx=xsinxsinx-xcosxdxsinx-xcosxxsinx1sin2x+cos2x=1tan2x+1=sec2xcot2x+1=csc2xa2-x2dx=x2a2-x2+a22arcsinxa+C??2??2????=??2??2??2??22ln|??+??2??2|+??dx(x2+9)3tan2x+1=sec2xx=3tantxt(-2,2)xtdx(x2+9)3=393cos4tdtcos4tdt??????????????cosx=sin(2-x)??????????????4cos4tdt=cos2t(1-sin2t)dt=cos2tdt-cos2tsin2tdt22-x2x4dxx=1t()d=-dd.dxearctanx(1+x2)32dx=earctanxx+x2-earctanx(1+x2)32dx=earctanxx+x2-[earctanx1+x2--xearctanx(1+x2)32dx]=earctanxx-1+x2-xearctanx(1+x2)32dxxearctanx(1+x2)32dx=x-12+x2earctanx+Csin(lnx)dx165eaxsinbxeaxcosbxPm(x)eaxPm(x)sinbxPm(x)cosbxPm(x)(lnx)nPm(x)arctanx?Pm(x)m5xxxexd)1(2Cxedexxedxxexdedxxedxxedxxedxxexedxxeexdxxxexxxxxxxxxxxxx11111111)1(1)1(1)1()1()1(2222()1171(1)b(x-a)mdx(a,bm)m=1b(x-a)mdx=bln|x-a|+Cm1b(x-a)mdx=b(x-a)-m+1-m+1+C(2)cx+d(x2+ax+b)ndx(a,b,c,dn)x2+ax+b????=????(??2+??2)??(173)????+1=12????2??(??2+??2)??+2??-12????2??????????1=dxx2+a2=1aarctanxa+C61dxx3+12dxx4+1=dx(x2+1)2-(2x)2=dx(x2+1+2x)(x2+1-2x)3dxx6+1(175)211sinmxcosnxdxmnsin2x+cos2x=1mn2cosxsin3x+cos3xdx=11+tan3xd(tanx)dxx3+1??????????????cosx=sin(2-x)????????????????????????????=????????-2??(1??????2-1)????=????????-1????-1-????????-2????????????????????sinmxcosnxdxm=-nsinmxcosnxdx(2)sin5xsin7xdx(3)11sin4xcos2xdx=sin2x+cos2xsin4xcos2xdx=1sin2xcos2xdx+1sin4xdx2dxsin(x+)sin(x+=1sin(-sin[(x+)-(x+]sin(x+)sin(x+dx=1sin(-[cos(x+sin(x+-cos(x+sin(x+]dx(3dxsin3x+cos3x=13[2sinx+cosx+sinx+cosxsin2x-sinxcosx+cos2x]dx=23dx2cos(x-4)+23-d(cosx-sinx)(cosx+sinx)2+17=232ln|sec(x-4)+tan(x-4)|-23arctan(cosx-sinx)+C4xxbxaxIdsincoscosxxbxaxIdsincoscos1xxbxaxIdsincossin221bIaI121dCxxbIaI---------121-aIbI221|sincos|ln)sincosd(sincos1dsincossincos-CxbxaxbxaxbxaxxbxaxaxbaIbI------212.|sincos|ln22221CxbaaxbxababI.|sincos|ln22222CxbabxbxabaaI5(1)=tanx2sinx=21+2cosx=1-21+2tanx=21-2dx=21+2()(2)=tanxsinx=21+2cosx=11+2()dx=11+2(dx2+sinx()=d2++1()31x(ax+b)(cx+d)?n8=(ax+b)(cx+d)?n1+x3dx=1x1+xxdxt=1+xx2xax2+bx+cax2+bx+cdx1+2+2x+2=dx1+(x+1)2+1x+1=tantABdx(a+bcosx)2=Asinxa+bcosx+Bdxa+bcosxAb+Ba+(Aa+Bb)cosx=1{Ab+Ba=1Aa+Bb=0a2b2A=-ba2-b2B=aa2-b2a2=b2,