The linearization problem of second-order nonlinear differential equations was first explored by Sophus Lie. In line with this research, he discovered that these equations must satisfy certain conditions to be linearized, and examined the structures of linearization transformations performed to fulfil these conditions. In this study, one of the transformation methods is performed by these conditions is discussed. It is shown that the linearized equations can be integrated by obtaining the first integrals. Then, the force-free Duffing-van der Pol oscillator is examined. The necessary conditions on parameters for the linearization of this equation are obtained, and the first integral of this equation was found.