Re: Can Mathematica NIntegrate a Log-type singularity?
- To: mathgroup at smc.vnet.net
- Subject: [mg92682] Re: Can Mathematica NIntegrate a Log-type singularity?
- From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
- Date: Fri, 10 Oct 2008 04:35:45 -0400 (EDT)
- References: <gckmrr$ng7$1@smc.vnet.net>
Aaron Fude <aaronfude at gmail.com> wrote:
> Hi,
>
> I would like to evaluate the following:
>
> NIntegrate[alpha^2 Log[2 Cos[alpha/2]]^2, { alpha, -Pi, Pi}]
>
> How do I help Mathematica deal with the LogSquared type singularity at
> either end of the interval. If I try it straight, Mathematica
> complains and gives a wrong answer.
When I try it straight, Mathematica 6 does not complain and gives an answer
which I suspect is correct.
> Please note, that Mathematica has absolutely no problem Integrating or
> NIntegrating the function
>
> Log[Cos[alpha/2]]^2
>
> from -Pi to Pi, each time giving the correct answer, but the multiple
> of alpha^2, throws it off.
>
> Many thanks in advance,
>
> Aaron.
>
> PS: By the way, I'm pretty sure that that integral must be some
> rational number times Pi^5.
It seems to be 11/90 * Pi^5.
David