Question

integral of lnx .....?????

Answer 1

solving through integration by parts

ln(x) dx

set 
  u = ln(x),    dv = dx 
then we find 
  du = (1/x) dx,    v = x

substitute

 ln(x) dx =  u dv

and use integration by parts

= uv -  v du

substitute u=ln(x), v=x, and du=(1/x)dx

= ln(x) x -  x (1/x) dx 
= ln(x) x -  dx 
= ln(x) x - x + C 
= x ln(x) - x + C.