  A simple method is outlined for analytic evaluation of the basic 2-electron
atomic integral with integrand containing products of atomic s-type Slater
orbitals and exponentially correlated function of the form $r_{ij}
exp(-\lambda_{ij}r_{ij})$, by employing the Fourier representation of
$exp(-\lambda_{ij}r_{ij})/r_{ij}$ without the use of either the spherical
harmonic addition theorem or the Feynman technique. This method is applied to
obtain closed-form expressions, in a simple manner, for certain other 2-,3- and
4-electron atomic integrals with integrands which are products of exponentially
correlated functions and atomic s-type Slater orbitals.
