       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:=
> Integrate[x^2 / E^(a*(1 - 2*x^2)^2), {x, 0, 1},
> Assumptions -> a >= 0]
>
> Out=
> (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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