  The mixmaster model has always been a field of controversy in the literature
regarding its (non)integrability. In this work, we make use of a generalized
definition of a class of nonlocal conserved charges in phase space to
demonstrate that the anisotropic Bianchi type IX model in vacuum is -at least
locally - Liouville integrable, thus supporting the findings of previous works
pointing to this result. These additional integrals of motion that we use can
be defined only due to the parametrization invariance of the system and can be
seen to possess an explicit dependence on time. By promoting the time variable
to a degree of freedom, we demonstrate the existence of two sets of four
independent conserved charges that are in involution, thus leading to the
characterization of the system as integrable in terms of the Liouville-Arnold
theorem.
