Re: [math-fun] An improper integral equals to log(\pi/2)-\gamma

I tried this in maxima using risch(log(x)/(1+cosh(x)),x): Maxima encountered a Lisp error: Error in PROGN [or a callee]: Caught fatal error [memory may be damaged] Automatically continuing. To reenable the Lisp debugger set *debugger-hook* to nil. Whoops! At 12:10 PM 2/17/2011, Warut Roonguthai 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