Use the standard Laplace transform,
You can just evaluate the rhs to confirm this. We want the instance where
, thus
What occurs when we use this in the context of a potential energy integral involving only 1s functions?
Conveniently, the laplace transform takes 
into a function with
the appearance of a 1s gaussian of orbital exponent s centered on
. A second application of the GPT and we can switch the order of
integration, evaluating the integral over s second.
Now making the substitution 
amazingly cancels just
about everything leaving
which everyone recognizes as a standard error function,
