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Re: Principal Value integral


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
>
>
>
>



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