From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Newsgroups: sci.math
Subject: Re: integral
Date: 22 Nov 1998 20:47:59 -0500

In article <365804DC.F13EFC0F@interport.com>,
ari abramowitz  <ari@interport.com> wrote:
>Who could help to resolve this integral:
>from zero to infinity of [x(x-1)]/ [(exp x)-1] dx
>Thanks you so much. It drives me crazy

Divide numerator and denominator by exp(x), and convert the integral into
the integral of an infinite sum (geometric series with quotient exp(-x)). 
The interchange of summation and integration is legitimate (find out why),
and you end up with a combination of values of the Zeta function. 

Good luck, ZVK(Slavek).
==============================================================================
[That's  2 Zeta(3) - Zeta(2). Here, Zeta(2)=Pi^2/6, but no closed form is
 known (or expected, I suppose) for the (irrational) number Zeta(3). - djr]