例3求 x(1+2nx) 解 d(nx) x(1+2lnx)”J1+2lnx 2J1+2lnx d(1+ 2Inx) u=1+2Inx j du=Inu+C=In(1+2Inx)+C 2u 2 2 上页例3 求 . (1 2ln ) 1 dx x x  + 解 dx x x  (1+ 2ln ) 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 = lnu + C 2 1 ln(1 2ln ) . 2 1 = + x + C