例3求 x x(1+2In x 解 x(1+2nx) d=∫,dmx) +2In d(1+2nx) 1+2Inx u=1+2nx du =Inu+C=In(1+2Inx)+C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 x = +1 2ln  = du u 1 2 1 = lnu + C 2 1 ln(1 2ln ) . 2 1 = + x + C