  This paper elaborates the integral transformation technique of [K. Pachucki,
W. Cencek, and J. Komasa, J. Chem. Phys. 122, 184101 (2005)] and uses it for
the case of the non-relativistic kinetic and Coulomb potential energy
operators, as well as for the relativistic mass-velocity and Darwin terms. The
techniques are tested for the ground electronic state of the helium atom and
new results are reported for the ground electronic state of the H$_3^+$
molecular ion near its equilibrium structure.
