Re: Simplification of definite integral?
- To: mathgroup at smc.vnet.net
- Subject: [mg40708] Re: Simplification of definite integral?
- From: Jon Harrop <jdh30 at cam.ac.uk>
- Date: Mon, 14 Apr 2003 04:06:10 -0400 (EDT)
- Organization: Univerisity of Cambridge
- References: <b7avdo$qlg$1@smc.vnet.net>
- Reply-to: jdh30 at cam.ac.uk
- Sender: owner-wri-mathgroup at wolfram.com
Dr. Wolfgang Hintze wrote:
> How do I get a satisfactory result from mathematica for this function
>
> f[d]:=Integrate[Sin[x-d]/(x-d) Sin[x+d]/(x+d),{x,-Infinity,Infinity}]
>
> I tried
>
> f[d]//ComplexExpand
>
> and several assumptions but I didn't succeed. Any hints?
It seems to work for me, the integral can only be taken with the following
assumption:
Integrate[Sin[x - d]/(x - d) Sin[x + d]/(x + d), {x, -\[Infinity],
[Infinity]}, Assumptions -> {Im[d] != 0}]//FullSimplify
gives:
(Cos[2*d]*(Log[-d^(-1)] - Log[d^(-1)]))/(2*d)
Cheers,
Jon.