       Re: troubling simple integral

• To: mathgroup at smc.vnet.net
• Subject: [mg91364] Re: troubling simple integral
• From: did <didier.oslo at hotmail.com>
• Date: Mon, 18 Aug 2008 03:37:25 -0400 (EDT)
• References: <g86844\$hr7\$1@smc.vnet.net> <g88v87\$gva\$1@smc.vnet.net>

```On Aug 17, 12:41 pm, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> Does the following result look better?
>
> In:= Assuming[x > 0 && Im[a] == 0 && Im[b] == 0 && Im[y] ==
= 0,
>   FullSimplify[
>    Integrate[(b + k*x)/k^2*Exp[-k*x]*Sin[k*a]*Sin[k*y], {k, 0,
>      Infinity}]]]
>
> Out= 1/4 (2 b ((-a + y) ArcTan[(a - y)/x] + (a + y) ArcTan[(a + y)/
>          x] - x ArcTanh[(2 a y)/(a^2 + x^2 + y^2)]) +
>     x Log[1 + (4 a y)/(x^2 + (a - y)^2)])

That looks much better indeed. Thanks.

> Note that *Assuming* passes the assumptions to both Integrate[] *and*
> FullSimplify[]. (In your original expression, only Integrate[] could
> take into account the assumptions.)

I understand that. But what I find puzzling the result obtained by Alberto
(I got the same). I'm wondering if there is an issue there.

```

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