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MathGroup Archive 2005

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Re: Help for an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57277] Re: Help for an integral
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 23 May 2005 02:20:46 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <d6k8mk$r3$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

at least you can do a indefined integration with
eqn = a(1 - 2*x^2)^2 == -z^2:

repl = Solve[eqn, x] // FullSimplify;

lstInteg = integ /. repl // FullSimplify;

lstDt = ((Map[Dt[#, Constants -> {a}] &, repl, 
{2}]) //.
          Verbatim[Dt][q_, Constants -> _] :> 
Dt[q]) /. ({_ -> b_}) :> b /.
            Dt[z] -> 1

Integrate[#, z] & /@ FullSimplify[#, a > 0] & /@ 
lstInteg*lstDt

if you insert the transformed boundaries you may 
get a solution,

if you look carefull to your integration path and 
the potential singularities

inside.

Regards

  Jens



"Valeri Astanoff" <astanoff at yahoo.fr> schrieb im 
Newsbeitrag news:d6k8mk$r3$1 at smc.vnet.net...
> Help needed :
> I can't - and Mathematica 5.0 can't either - 
> integrate this :
>
>
> In[1]:=
> Integrate[x^2 / E^(a*(1 - 2*x^2)^2), {x, 0, 1}, 
> Assumptions -> a >= 0]
>
> Out[1]=
> (2*Integrate`TableDump`c$70*E^Integrate`TableDump`c$70^2 
>  -
> 
> Sqrt[Pi]*Erfi[Integrate`TableDump`c$70])/E^(5*a)/
>  (4*Integrate`TableDump`c$70^3)
>
>
> Thanks in advance for any hint.
>
> v.a.
> 



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