Re: Can Mathematica NIntegrate a Log-type singularity?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92666] Re: [mg92642] Can Mathematica NIntegrate a Log-type singularity?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 10 Oct 2008 04:32:50 -0400 (EDT)*Reply-to*: hanlonr at cox.net

$Version 6.0 for Mac OS X PowerPC (32-bit) (June 19, 2007) nint = NIntegrate[alpha^2 * Log[2 Cos[alpha/2]]^2, {alpha, -Pi, Pi}] 37.4024 nint/Pi^5 0.122222 % // Rationalize 11/90 The result is stable for changes in WorkingPrecision. The integral appears to be 11/90 * Pi^5 Bob Hanlon ---- 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. 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. -- Bob Hanlon