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MathGroup Archive 1998

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  • To: mathgroup at
  • Subject: [mg12741] Integration
  • From: Carl Woll <carlw at>
  • Date: Fri, 5 Jun 1998 02:04:20 -0400
  • Organization: University of Washington
  • Sender: owner-wri-mathgroup at

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] 


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

Carl Woll
Dept of Physics
U of Washington

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