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 > > > > >

**References**:**Integration of Exp[-x^2]/(1 + Exp[a * x])***From:*"Stefan" <themailingman@yahoo.de>