  We study the holonomy cocycle H of a holomorphic foliation \Fc by Riemann
surfaces defined on a compact complex projective surface X satisfying the
following two conditions:
  1) its singularities E are all hyperbolic;
  2) there is no holomorphic non-constant map \C\to X such that out of E the
image of \C is locally contained in a leaf.
  Let T be a harmonic current tangent to \Fc which does not give mass to any
invariant analytic curve. Using the leafwise Poincar\'e metric, we show that H
is integrable with respect to T.
  Consequently, we infer the existence of the Lyapunov exponent function of T.
