例4求 dx e2+e°+e 解令巴=,x=6lmt,d=t, 6 原式= 6 dt t°+t+t r(1+t)(1+t2) 6 AB Ct+D 设 (1+1)(1+t2)tt+11+t2 6=A(1+t)(1+t2)+Br(1+t2)+(Ct+D)t(t+1)例 4 解 . 1 2 3 6  + + + x x x e e e dx 求 , 6 e t x 令 = x = 6ln t , , 6 dt t dx = dt t t t t6 1 13 2  + + + = 原式  dt t t t  + + = (1 )( 1 ) 6 2 2 2 (1 )(1 ) 1 1 6 t Ct D t B tA t t t ++ + + = + + + 设6 (1 )(1 ) (1 ) ( ) ( 1) 2 2 = A + t + t + Bt + t + Ct + D t t +