Let A(p) be the class consisting of functions f that are holomorphic in D{p}, p ∈ (0, 1) possessing a simple pole at the point z = p with nonzero residue and normalized by the condition f(0) = 0 = f′ (0) − 1. In this article, we first prove a sufficient condition for univalency for functions in A(p). Thereafter, we consider the class denoted by Σ(p) that consists of functions f ∈ A(p) that are univalent in D. We obtain the exact value for ∆(r, z/ f), where the Dirichlet integral ∆(r, z/ f) is given by max f∈Σ(p) ∫∫ ∆(r, z/ f) = |z|<r |(z/ f(z))′ |2 dx dy, (z = x+iy), 0 < r ≤ 1. We also obtain a sharp estimate for ∆(r, z/ f) whenever f belongs to certain subclasses of Σ(p). Furthermore, we obtain sharp estimates of the integral means for the aforementioned classes of functions.