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>
- Reply-to: kuska at informatik.uni-leipzig.de
- 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,
>
> Thanks in advance, Stefan