Analytic Evaluation of Three Different Five-Electron Atomic Integrals Involving Exponentially Correlated Functions of $r_{ij}$ With $r_{ij}$'s Not Forming A Closed Loop

The simple method outlined in our earlier paper [B.Padhy, Orissa Journal of Physics, vol.19, No.1, p.1, February 2012] has been utilized here for analytic evaluation of three different five-electron atomic integrals with integrands involving products of s Slater-type orbitals and exponentially correlated functions of the form $r_{ij}exp(-{\lambda }_{ij}{r}_{ij})$. Only products of those $r_{ij}$'s which do not form a closed loop by themselves, are considered.