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Principal Value integral

• To: mathgroup at smc.vnet.net
• Subject: [mg52361] Principal Value integral
• From: Carlo Teubner <AskMeAndIllTellYou. at example.com>
• Date: Wed, 24 Nov 2004 02:32:35 -0500 (EST)
• Organization: Oxford University, England
• Sender: owner-wri-mathgroup at wolfram.com

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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