Hi there, I would like to solve the integral:
NIntegrate[( Sqrt[12 ((x - y)^2/(x + y)^2 + (x - z)^2/(x + z)^2 + (y - z)^2/(y + z)^2)]
Boole[Sqrt[1/3 ((x - y)^2/(x + y)^2 + (x - z)^2/(x + z)^2 + (y - z)^2/(y + z)^2)] == a])/
(E^(x + y + z) Sqrt[(-((4 x (x - z))/(x + z)^3) - (4 y (y - z))/(y + z)^3)^2 + ((4 z (y - z))/(y + z)^3 -
(4 x (x - y))/(x + y)^3)^2 + ((4 y (x - y))/(x + y)^3 + (4 z (x - z))/(x + z)^3)^2]),
{x, 0, \[Infinity]}, {y, 0, \[Infinity]}, {z, 0, \[Infinity]}]
With parameter $a\in [0,1]$. But the expression above does not work.
I have also tried by creating an implicit region of the surface where I'm integrating (mainly the expression inside the Boole operation), but it fails to discretize the region.
Do you know what I might be doing wrong? Do you know any work-around? Any advice is welcome.
