1728 1 解 +1 5-4x+3x-2x2+x-ln1+x1+C 1729 x+1+√x-1 dx x+1 (√x+1 )dx 〔x+1)-(x-1))+C 1730.x√2-5xdx 解 MCC.I (2-5x)+÷](2-5x)dx (2-5x)2+=(2-5x)2dax (2-5x)是4 75 (2-5x)2+C 125 8+30x 375(2-5x)2+C. 1731. Ca rd 解 1「(l dx 1-3x (1-3x) 〔(1-3x)3一(1-3x)-dx 26
16(1-3x)3-(1-3x)3+C L+2 10(1-3x)3+C. 1732.x3y1+x2dx 解jxy+xdx 1(x2+1)-1(+x)a(1+x 2(1+x)-(1+x)d(1+x) 3(1+x2)-3(1+x2)+C 12x2-9 56(1+x2)+C. 1733 dr (x-1)(x+3) 解 d (x-1)(x+3)4 +3 dx 4|x+3 O dx 1734.x+x-2 解∫x4 x x-2 +2 d =3l|x+2|+C 1735 (x2+1)(x2+2) dx 解 (x2+1)(x2+2) x tl 2 dr 27
arc tg.r arc tg -+C 1736 2)(x2+3) 解 d 2)(x2+3) dx 2x2+3 ctg + C rd? 1737 (x+2)(x+3) 解 (x+2)(x+3) +3x+2 =hnx+3|3 (x+2)2 +C dr 1738. +3x2+2 解 rdx x+3x2+2-2J(x2+1)(x2+2) 2Jx2+1x2+2 C d 9. J(x+a)(x+b) (a≠b) 解 (x+a)2(x d b)2(x+ax+4 十 (a-b)2小((x+a)2(x+b)2 2 (x+a)(x+b) dx 28
2L.cosa-cos(2 xta))dx x cosa sin(2x+a)+C. 1744 解 snn5x·s1n5x三 (cos 2x-cos &x)dr 2r-isin8x+C. 1745.lcos·cosd 解 5C cos cos dx= cOs Tcos 6 =3sin 5+3sin I +C 1746.sin2x 6)·cos(3x)dx 解 sin 6/·cos3x+dx 5丌 sin! 5x+ sIn cos 5r+12)+2 cos +12 +C 1747. sinxdr. 解|sinx (cos2r-1)d(cos r) os cosT 1748 d * xdx=(1-sin2x)d(sinr 30
= =sin. sinr+C 1749. sin'xdx. 解 cos 2r12 sinrd r= dx cos 4r 2cos2x十 idr =I(3-4cos2x+cos4x)d 3 8atsin2xtoosin4x+C. 1750.cos·adx. 解 1+cos 2x cos rdr 2 1+2cos2r-+ 1+ cos 4-r 2 8」(3+4cos2x+cos4x)d 3 cr+isin 2x+oesin4r+C 32 1751.ctg rdx. M ctg2rdx=l(csc2x-1)dx=-ctgx-x+C 1752. tg'xdx w tgrdx=tgr.(sec@r-1)dx tgxd(tgr)-tgIdx 528x+in cosr+c, 31