Liouvillian first integrals for generalized Liénard polynomial differential systems

Agraïments/Ajudes: The second author has been partially supported by FCT through the project PTDC/MAT/117106/2010 and through CAMGD, Lisbon.We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' = −g(x) − f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f