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Re: Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1

• To: mathgroup at smc.vnet.net
• Subject: [mg52393] Re: [mg52340] Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
• From: DrBob <drbob at bigfoot.com>
• Date: Thu, 25 Nov 2004 05:50:46 -0500 (EST)
• References: <200411240732.CAA28785@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

All but the first is divergent on -oo to oo, while the first is zero.

NIntegrate should handle this very well for finite limits. For instance:

Clear[f]
f[n_Integer][x_] :=
   (Exp[-(x - m)^2/(2*s^2)]*x^n)/(1 + x^2)
NIntegrate[f[2][x] /. {m -> 0, s -> 1}, {x, -5, 2}]
0.8149597066587511

NIntegrate[f[1][x] /. {m -> 0, s -> 1}, {x, -5, 5}]

0.

Bobby

On Wed, 24 Nov 2004 02:32:11 -0500 (EST), Opps <*cutinbetweenasterixes*theopps75*evenhere* at *thisalso*yahoo.it> wrote:

> Hi,
>     any suggestion to make the integral of:
>
> Exp[-(x-m)^2/(2 s^2)] x (1+x^2)^-1
> Exp[-(x-m)^2/(2 s^2)] x^2 (1+x^2)^-1
>
> Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
>
>
>
> between -inf and +inf (or indefinite)?
>
> Look like it is not possible, but it is too long time I do not make
> integrals with more advanced techinques (as going to the complex plane)...
> so if you have suggestions (wonderful a solution :) )....
>
> THANKS
>
> Ale
>
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net

• Follow-Ups:
  • Re: Re: Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
    • From: DrBob <drbob@bigfoot.com>

• References:
  • Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
    • From: "Opps" <*cutinbetweenasterixes*theopps75*evenhere*@*thisalso*yahoo.it>