  Context: The modelling of stationary galactic stellar populations can be
performed using distribution functions.
  Aims: This paper aims to write explicit integrals of motion and distribution
functions.
  Methods: We propose an analytic formulation of the integrals of motion with
an explicit dependence on potential. This formulation applies to potentials
with rotational symmetry or triaxial symmetry. It is exact for St\"ackel
potentials and approximate for other potentials.
  Results: Modelling a stationary stellar population using these integrals of
motion allows the force field to be found with satisfactory accuracy. On the
other hand, the mass density distribution that generates the force field and
the gravitational potential is recovered with less accuracy due to lower
precision in modelling box-type orbits.
