  We present details of logically simplest integral sufficient for deducing the
Stirling asymptotic formula for n!. It is the Newton integral, defined as the
difference of values of any primitive at the endpoints of the integration
interval. We review in its framework in detail two derivations of the Stirling
formula. The first approximates log(1)+log(2)+...+log(n) with an integral and
the second uses the classical gamma function and a Fubini-type result. We
mention two more integral representations of n!.
