what is the issue in evaluating two electron integral?
The main problem of 2-electron integrals is their amount. They are given by

\begin{equation}
  I_{ijkl} = \langle ij|r^{-1}_{12}|kl\rangle 
\end{equation}

where $i$, $j$, $k$ and $l$ run over all $N$ atomic orbitals. So we need to calculate $\mathcal{O}(N^4)$ integrals, which makes this a bottleneck (in terms of memory and computing time).

For Gaussian Type Orbitals we can evaluate the integrals analytically, which is much faster than numerical approaches. But this does not help with the $N^4$ scaling.

Evaluation for Gaussian Type Orbitals is explained in Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund for s orbitals ($l=0$). More general evaluation schemes for higher angular momentum are explained in detail in Molecular Electronic-Structure Theory by Helgaker, Jorgenson and Olsen.