Victor H. Moll brought my attention to his paper: A class of logarithmic integrals Ramanujan Journal 20, 2009, 91-126 available at http://129.81.170.14/~vhm/web_html/finallog.pdf With some transformations, the integral in question is equivalent to Example 7.6. Warut On Fri, Feb 18, 2011 at 3:10 AM, Warut Roonguthai <warut822@gmail.com> wrote:

Can anyone tell me how to prove that

\int_0^\infty log(x)/(1+cosh(x)) dx = log(\pi/2)-\gamma?

Any info related to this integral is also appreciated. I could find nothing except that Wolfram|Alpha knew it.

Hope that this isn't too trivial for math-fun.

Thanks, Warut