How can one show the multiple integral $\int_{0}^{a} \int_{0}^{a} \frac{dx ~ dy}{(a^2+x^2+y^2)^{3/2}}= \frac{\pi}{6a}$ by hand?
Double Integral $\int\limits_0^a\int\limits_0^a\frac{dx\,dy}{(x^2+y^2+a^2)^\frac32}$