Since the potential energy is due to coulombic interaction of the nuclei
with the electron in question, the operator to deal with is 
. Thus
the integral we need to evaluate is
Since the operator does not affect the operand (
), we can combine the
two orbitals via the gaussian product theorem, and make the final statement
where 
. This is still
intractible, since we've failed to write everything in terms of the
integration variables, 
. At this point, we want to apply some sort of
transform to the 
to turn it into some sort of an
exponential which can be combined with the other gaussians and result in
resolution of the variables. There are two standard possibilities -- the
one I like and the one everyone uses. First things first...