WRITE      log X /(1+X)^2   as

logx - log(1+x)^2

using property of log

logx - 2log (1+x)

now the resulting integral is

   - 2[xlnx]1 to 3 + 1/1+xdx

now put values and get answer

please rate me.

Apply by parts taking logx as the first and ( 1+x)^-2 as the second fn .

in the later integral int ( 1/( x (x+1)) dx write it as int dx/x - int dx/(x+1)

which is easily integrable ( formula)

As fenymann sir said,Solve using by parts,It becomes,

=-ln3/4+ln3-ln4+ln2=3ln3/4-ln2=ln27-ln16/4=(1/4)ln(27/16).