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

• To: mathgroup at smc.vnet.net
• Subject: [mg39635] Re: Integration of Exp[-x^2]/(1 + Exp[a * x])
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 27 Feb 2003 00:27:15 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <b3hs7u\$iki\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

if Exp[a*x] < 1 you can try a geometric series, i.e.,

1/(1+Exp[a*x})= Sum[(-Exp[a*x])^n,{n,0,Infinity}]

and integrate

term=Integrate[Exp[-x^2]*(-Exp[a*x])^n, x]

and work with

Sum[Evaluate[term], {n, 0, Infinity}]

for a<0 the sum should be quickly convergent.

Regards
Jens

Stefan wrote:
>
> 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,
>

```

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