During one of my practical courses we had to do the Hartree-Fock-method "by hand". Part of that was to calculate the occurring two electron integrals.
With $$\chi_i(r) = 2 \cdot \alpha_i^{3/2} e^{-\alpha_i r} Y_0^0$$ we were given the following equation: $$\iint \frac{\chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)}{|r_1-r_2|}~\mathrm d r_2 \mathrm d r_1$$ $$= 16\pi^2\int_0^{\infty}\int_0^{r_1} \chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)~r_1~r_2^2~\mathrm d r_2 \mathrm d r_1$$ $$+ 16\pi^2\int_0^{\infty}\int_{r_1}^{\infty} \chi_m(r_1)~\chi_n(r_1)~\chi_t(r_2)~\chi_u(r_2)~r_1^2~r_2~\mathrm d r_2 \mathrm d r_1$$
What are the steps to come up with this? (At least I know where the $16\pi^2$ come from $\ldots$)