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MathGroup Archive 2003

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Re: Integration of Exp[-x^2]/(1 + Exp[a * x])

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39643] Re: [mg39623] Integration of Exp[-x^2]/(1 + Exp[a * x])
  • From: "Christophe Le Poncin-Lafitte" <leponcin at danof.obspm.fr>
  • Date: Thu, 27 Feb 2003 00:28:12 -0500 (EST)
  • References: <200302260743.CAA18986@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Stefan,

your problem is quiet difficult.
There's no analytical solution for this integral, as far I know ; You can
consult the book of Ryzhik and Gradshteyn, wich is a very good table of
integrals, and your situation does not exist.
But you have the identity :

Integrate[Exp[-x^2]/(1+Exp[a*x]),{x,-Infinity,Infinity}]=Sqrt[Pi]/2  if
Re[a]>0

An indefinite integral of this type can not be calculated by Mathematica.
Maybe, you have to do an analytical work with integration by parts, before
the evaluation of integral with Mathematica. Or, if any mathematical
solution is possible, you have the last way with numerical method.

Christophe

------------------------------
Christophe Le Poncin-Lafitte

Observatoire de Paris
Dpt Systèmes de Référence Temps et Espace
Equipe "Theorie relativiste des systèmes de Références"


----- Original Message -----
From: "Stefan" <themailingman at yahoo.de>
To: mathgroup at smc.vnet.net
Subject: [mg39643] [mg39623] Integration of Exp[-x^2]/(1 + Exp[a * x])


> Hello,
>
>
>
> I have to integrate the function Exp[-x^2]/(1 + Exp[a * x]) where a is
> real-valued parameter. Unfortunately
>
>
>
> Integrate[Exp[-x^2]/(1 + Exp[a * x]), x]
>
>
>
> yields no results. Does anyone know a clever trick I might have missed?
Any
> hint would be welcome,
>
>
> Thanks in advance, Stefan
>
>
>
>
>




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