Re: Principal Value integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg52395] Re: [mg52361] Principal Value integral*From*: DrBob <drbob at bigfoot.com>*Date*: Thu, 25 Nov 2004 05:50:53 -0500 (EST)*References*: <200411240732.CAA28890@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Version 5.1 gets your desired result: Integrate[1/(x^3 - 1), {x, -Infinity, Infinity}, PrincipalValue -> True] -(Pi/Sqrt[3]) Bobby On Wed, 24 Nov 2004 02:32:35 -0500 (EST), Carlo Teubner <"AskMeAndIllTellYou."@example.com> wrote: > The following Principal Value integral does not appear to give the > correct result. > > Integrate[1/(x^3-1), {x, -Infinity, Infinity}, PrincipalValue->True] > > This gives I Pi / 3, which surely can't be right since the answer should > be real. > > When doing it numerically, it gives the right answer: > > <<NumericalMath`CauchyPrincipalValue` > CauchyPrincipalValue[1/(x^3-1), {z, -Infinity, {1}, Infinity}] > > This gives -1.8138 which is the correct answer (it's -Pi/Sqrt[3]). > > Any explanations? Is this a bug or am I missing something? > > Carlo > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Principal Value integral***From:*Carlo Teubner <AskMeAndIllTellYou.@example.com>