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MathGroup Archive 1998

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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



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