  In this paper we revisit a Poincare lemma for foliated forms, with respect to
a regular foliation, and compute the foliated cohomology for local models of
integrable systems with singularities of nondegenerate type. A key point in
this computation is the use of some analytical tools for integrable systems
with nondegenerate singularities, including a Poincare lemma for the
deformation complex associated to this singular foliation.
