The radio physical oscillator model is a three-dimensional autonomous system of first-order ordinary differential equations with a nonlinear but quintic polynomial. This model describes a generator of hard oscillations with coupled to a rechargeable power source and depending on four nonnegative parameters. The Darboux integrability of this system is studied in this research. More particularly, we characterize all the invariant algebraic surfaces and the exponential factors of this system. We show that for any value of parameters the radio physical oscillator system does not admit polynomial, rational and Darboux first integrals through the analysis of its Darboux polynomials and its exponential factors.