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integrate log*sinc

• To: mathgroup at smc.vnet.net
• Subject: [mg109194] integrate log*sinc
• From: pimeja <sed.nivo at gmail.com>
• Date: Fri, 16 Apr 2010 05:52:35 -0400 (EDT)

Hi All,

For Integrate[Log[x] Sin[x]/x, {x, 0, \[Infinity]}] Mathematica
returns -EulerGamma \[Pi].
How to proof this analytical?

I've tried to use residue theory but it seems not suitable since
integrand has pool of second order in zero (for Jordan lema should be
first order only). Substitution x=Exp[y] returns even more strange
result.

Thanks in advance.