I have to calculate this integral $\int \frac{d S_q d S_p}{1 + a^2 +(\overline{q}+\overline{p})^2}$
Where $\overline{p},\overline{q}$ unit n-dimensional vectors. Integration goes over n-1 unit dimensional spheres. a^2 is taken so that integral converges
I found exact form in 2D. In bigger dimensions i tried to use hyperspherical coordinates, but was not able to find the answer