例3求 dx x(1+2In x) 解 dx x(1+2In x) d(n x) 1+2Inx d(1+ 2In x) 21+2In x u=1+2Inx 1。1 a-du =Inu+C= In(1+2Inx+C L 2 2 上页例3 求 . (1 2 ln ) 1 d x x x  + 解 d x x x  (1 + 2 ln ) 1 (ln ) 1 2ln 1 d x x  + = (1 2ln ) 1 2ln 1 2 1 d x x + + =  u = 1+ 2ln x  = du u 1 2 1 = ln u + C 2 1 ln(1 2ln ) . 2 1 = + x + C