I was doing a physics problem and came across this integral which i need to solve
$$I(x,y,z)=\int_0^{2\pi}\int_0^{2\pi}\int_0^{2\pi}\left(\frac{1}{8\pi^3}\right)\left(\frac{1-\cos(nx+my+pz))}{3-\cos(x)-\cos(y)-\cos(z)}\right)dx\,dy\,dz$$
What i want to know is that does this integral evaluate to any specific function $f(n,m,p)$, and if so then how to calculate it?
I tried Wolframalpha's triple integral calculator but that doesn't seem to work..
Are there any other online applications i can use to calculate such integrals?