Let R be a commutative Noetherian ring with identity. I. Swanson proved in() that every ideal in every commutative Noetherian ring has linear growth of primary decompositions. Later, in(), R.Y. Sharp generalized this result to finitely generated modules over R. In the first section we present another (may be simpler) proof of this generalized result. Sharp also proved in() that every proper ideal in R has linear growth of primary decompositions for integral closures of ideals. We extend, in the last section, this result to finitely generated modules over R.