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