Careful where your dx is, there. Can you give the command in Mathematica that gave you 1 + 2 ln(2)? I'm getting the first answer in Mathematica.
I get two different solutions for the integral
depending on how I evaluate it. Series expansion gives while Mathematica gives as an analytical as well as a numerical solution. On the other hand, Wolfram Alpha also gives . I'm thinking that there must be some problem with singularities and/or (non)uniform convergence of the Taylor series for the logarithm.
Any thoughts will be much appreciated.