  This paper explains the fundamental relation between Jacobi structures and
the classical Spencer operator coming from the theory of PDEs so as to provide
a direct and geometric approach to the integrability of Jacobi structures. It
uses recent results on the integrability of Spencer operators and
multliplicative forms on Lie groupoids with non-trivial coefficients. In
Theorem 1 we show that the Spencer operator associated to a contact groupoid
reveals that the base manifold carries a Jacobi structure. Theorem 2 deals with
the problem of integrating Jacobi structures to contact groupoids.
