In this study, we consider a Lienard II-type harmonic nonlinear oscillator equation as a nonlinear dynamical system. Firstly, we examine the first integrals in the form A(t, x)(x)over dot + B( t, x), the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the lambda-symmetry approach. We show that the equation can be linearized by means of a nonlocal transformation, the so-called Sundman transformation. Furthermore, using the modified Prelle-Singer approach, we point out that explicit time-independent first integrals can be identified for the Lienard II-type harmonic nonlinear oscillator equation.