Degree of the first integral of a pencil in ℙ² defined by lins neto

Let P₄ be the linear family of foliations of degree 4 in ℙ² introduced by A. Lins Neto, whose set of parameter with first integral Ip(P₄) is dense and countable. In this work, we will compute explicitly the degree of the rational first integral of the foliations in this linear family, as a function of the parameter.