⑩串紫学 Teaching Plan on Advanced Mathematics 例3求2xeth uEx 解:「2xe2dk=[e2 d(x)=edu=e"+C=e+C 例4求 x(1+2Inx 解: d(n x) x(1+2Ix) 1+2lx - d(1+2In x) 2J1+2Inx u=1+2Inx reJduslnutc=In(1+2In x)+C 2 2Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例3 求  xe dx x 2 2 解：    = xe dx = e d x = e du u u x x x 2 2 2 2 ( ) 2 e C e C u x = + = + 2 求 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 = ln u+C 2 1 ln(1 2ln ) . 2 1 = + x +C 例4 dx x x  (1+ 2ln ) 1