  We present results expressing conditions for the existence of meromorphic
first integrals for Pfaff equations of arbitrary codimension, integrable or
not, on complex manifolds. These results are in the same vein as previous ones
by J-P. Jouanolou and E. Ghys. We also prove an enumerative result counting the
number of hypersurfaces invariant by a projective holomorphic foliation with
split tangent sheaf.
