In the present paper we address a relaxation theorem for a new integral functional of the calculus of variations de ned on the space of functions in W1;p loc whose gradient is an Lp-vector eld with distributional divergence given by a Radon measure. The result holds for integrand of type f(x; u) without any coerciveness condition, with respect to the second variable, and C1-continuity assumptions with respect to the spatial variable x.