Liouvillian integrability of a general Rayleigh-Duffing oscillator

We give a complete description of the Darboux and Liouville integrability of a general Rayleigh-Duffing oscillator through the characterization of its polynomial first integrals, Darboux polynomials and exponential factors.The authors are grateful to the referees for their valuable comments and suggestions to improve this paper. The first author is partially supported by a MINECO/ FEDER grant number MTM2017- 84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276. The second author is supported by FCT/Portugal through UID/MAT/04459/2013