Integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg12741] Integration*From*: Carl Woll <carlw at fermi.phys.washington.edu>*Date*: Fri, 5 Jun 1998 02:04:20 -0400*Organization*: University of Washington*Sender*: owner-wri-mathgroup at wolfram.com

Hi all, There's a simple definite integral which I can do through a simple change of variable, but Mathematica is unable to do. The integral is Integrate[ Exp[-x] Log[1 - Exp[-x]], {x,0,Infinity}] which if one makes the change of variables y = 1-Exp[-x] becomes Integrate[ Log[y], {y,0,1}] which equals -1. Why is it that Mathematica is unable to do this integral, and is there an option one can set which enables Mathematica to perform this integral and more general variants of it? Even worse is the following result which Mathematica gives for a slightly more general case Integrate[Exp[-a x] Log[1 - E[-x]],{x,0,Infinity}] Mathematica's answer for this integral is Indeterminate, but the integral clearly converges for a>0 (I think it actually converges for a>-1). Carl Woll Dept of Physics U of Washington