  Explicitly correlated quantum chemical calculations require calculations of
five types of molecular integrals beyond the standard electron repulsion
integrals. We present a novel scheme, which utilises general ideas of the
McMurchie-Davidson technique, to compute these integrals when the so-called
\range-separated" correlation factor is used. This correlation factor combines
the well-known short range behaviour, resulting from the electronic cusp
condition, with the exact long-range asymptotics found for the helium atom [M.
Lesiuk, B. Jeziorski, and R. Moszynski, J. Chem. Phys. $\textbf{139}$, 134102
(2013)]. Almost all steps of the presented procedure are formulated
recursively, so that an efficient implementation and control of the precision
are possible. Additionally, the present formulation is very flexible and
general, and it allows for use of an arbitrary correlation factor in the
electronic structure calculations with minor or no changes.
