??? E E EBBBccc<<<lllsss x1ííí k k kKKK<<<lllsss 1 p/ í ks￥′: (1) R+12 1x2?1dx; (2) R+11 dxx(1+x2); (3) R+10 xe?ax2dx(a > 0); (4) R+10 e?ax sinbxdx(a > 0); (5) R+10 px 1+x2dx; (6) R+10 dx(x2+p)(x2+q)(p;q > 0): 2) ?/ s￥ l ??: (1) R+10 dx3px4+1; (2) R+11 xarctanx1+x3 dx; (3) R+11 sin 1x2dx; (4) R+10 dx1+xjsinxj; (5) R+10 x1+x2 sin2 xdx; (6) R+10 xm1+xndx(n;m > 0); (7) R+10 x2dxx4?x2+1; (8) R+11 dxx 3p1+x2; (9) R+10 xpe?xdx;(p ? 0); 1 (10) R+11 lnxxp dx; (11) R+11 lnn xx2 dx(n); (12) R+10 sin2 xx dx; (13) R+10 cosax1+xn dx; (14) R+11 [ln(1+ 1x)? 11+x]dx; (15) R+11 ln(cos 1x +sin 1x)dx; (16) R+10 1x2 ln(1? sin2 x2 )?1dx: 3) ?/ í ks￥ l ??( ? ' l ?Hq l ?): (1) R+11 cos2 xx dx; (2) R+11 cosxx dx; (3) R+11 cosxxp dx; (4) R+10 pxcosx x+100 dx; (5) R+12 lnlnxlnx sinxdx: 4 !f(x) ? h(x) ? g(x);a ? x < +1;h(x) ?iμK uW[a;A] V ,?R+1a f(x)dx?R+1a g(x)dx l ?, p￡R+1a h(x)dx l ?. 5￡ ü? ?11.2,i  è a ü  I ^?? ?￥. 6 ?f(x)[a;+1) ??/?, OsR+1a f(x)dx l ?, p ￡: limx!+1xf(x) = 0: 7 !f(x)[0;+1) Bá ??,i OsR+10 f(x)dx l ?,￡ ülimx!+1f(x) = 0. ?T????sR+10 f(x)dx l ?,[#f(x)[a;+1) ? 2 ?,f(x) ? 0, ^? ˉμlimx!+1f(x) = 0? 8 !R+1a f(x)dxDR+1a f0(x)dx l ?, p￡: limx!+1f(x) = 0: 9 !f(x)??/? t? ,,f0(x)[0;+1) ??. p￡: Z +1 0 f0(x)sin2 xdx l ?. 10 !f(x)?g(x) ^?l[a;+1) ￥f ?, O ?? μK uW[a;A]  V,￡ ü: ?R+1a f2(x)dxDR+1a g2(x)dx l ?,5R+1a [f(x)+g(x)]2dxDR+1a f(x)g(x)dx9 l ?. 11￡ ü: (1) !f(x)[0;+1) ??, Olimx!+1f(x) = k,5 Z +1 0 f(ax)?f(bx) x dx = [f(0)?k]ln b a (b > a > 0): (2) ?  ?Hqlimx!+1f(x) = k?1R+1a f(x)x dxi(a > 0),5 Z +1 0 f(ax)?f(bx) x dx = f(0)ln b a (b > a > 0): x2<<<sss 1/ s ^? l ?? ? l ? p ′. (1) R 1 20 cotxdx; (2) R10 lnxdx : 3 (3) Ra0 dxpa?x; (4) R10 q x 1?xdx: 2) ?/ s￥ l ??: (1) R10 sinxx3 2 dx; (2) R10 dx3px2(1?x); (3) R10 lnx1?x2dx; (4) R … 20 dx sin2 xcos2 x; (5) R10 jlnxjpdx; (6) R … 20 1?cosx xm dx; (7) R10 dxlnx; (8) R…0 dxpsinx; (9) R10 xfi lnxdx; (10) R10 xp?1?xq?1lnx dx; (11) R … 20 ptanxdx; (12) R … 20 cosxlnsinxdx: 3 ?Y l ??: (1) R+11 ln(1? 1x2)?1dx; (2) R+10 xp?1e?xdx; (3) R+10 (arctanx)qxp dx; 4 (4) R+10 ln(1+x)xp dx; (5) R+11 dxxp lnq x; (6) R+10 dxxp+xq; (7) R+10 dx3px(x?1)2(x?2); (8) R0?1ex lnjxjdx: 4) ?/ s￥ l ??D ' l ??: (1) R+10 sinx2dx; (2) R+10 sinp xxq dx; (3) R+10 xp sinx1+xq dx(q ? 0); (4) R+10 sin(x+1x)xn dx: 59 ?/ <s￥′: (1) R10 (lnx)ndx; (2) R10 xnp1?xdx: 6￡ üsA = R … 20 ln(sinx)dx l ?,i p ′. 7 ?¨ 52T￡ ü: (1) R…0 ln(sin )d = ?…22 ln2; (2) R…0 sin 1?cos d = 2…ln2; (3) R … 20 sin2 ln(sin )d = … 4( 1 2 ?ln2); (4) R10 ln(1+x)1+x2 dx = …8 ln2: 5 8￡ ü?? T: (1) 12(1? 1e) < R+10 e?x2dx < 1+ 12e; (2) …2p2 < R10 dxp1?x4 < …2: 6