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I am currently working on a project, and I need to calculate the definite triple integral of 1/|x+y+z|. i.e:

int int int (1/sqrt((x-x')^2+(y-y')^2+(z-z')^2)) dx dy dz.

I have solved the integral, and it has 48 terms if the limits are inserted (6 terms with 3 sets of upper and lower limits). The computing power to model with this huge expression is too much, so is there a trick or shortcut that outputs a simple answer, even if it is slightly approximated?

Assistance would be greatly appreciated.

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# Extremly long Definite triple integral

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