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six-fold integral

• To: mathgroup at smc.vnet.net
• Subject: [mg30083] six-fold integral
• From: seidov at bgumail.bgu.ac.il (Zakir F. Seidov)
• Date: Fri, 27 Jul 2001 03:52:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Can anybody prove or disprove this result
 (Int_0^1\[Equal]Integral from zero to 1):

Int_0^1 Int_0^1 Int_0^1 Int_0^1 Int_0^1 Int_0^1
[(x-X)^2+(y-Y)^2+(z-Z)^2]^(-1/2) dx dy dz dX dY dZ =
(2 3^(1/2)-2^(1/2)-1)/5+pi/3 +
ln[(2^(1/2)-1)(2-3^(1/2)]?

This is a particular case 
of the general integral considered in:
arxiv:astro-ph/0002496.

The way I've got this result is 
the too lengthy interactive session
with MATHEMATICA - and IS NOT ELEGANT (though result is).

I beleive that result is correct 
but will be happy to hear from
anyone who could find the more elegant way to
prove or disprove this result.

Thanks a lot!!!!!!!!!!!!!

Also, e-mail messages are kindly welcome. 

Zakir F.Seidov
seidov at bgumail.bgu.ac.il
zfseidov at ycariel.yosh.ac.il
seidovzf at yahoo.com