Complexity in computing the integrals involving higher angular momentum
It appears that the integrals that are difficult are the two-electron repulsion integrals. There exists a recursive relationship that can turn integrals with high-angular momentum functions into integrals with only s-type functions. Refer to this lecture for details.

See the following articles for details concerning these recurrence relations:

M. Head Gordon and J. Pople, J. Chem. Phys. 89, 5777 (1988)

S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986)