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>