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Let $\mathcal{P}_4$ be the linear family of foliations of degree 4 in$\mathbb{P}^2$ given by A. Lins Neto, whose set of parameters with firstintegral $I_p(\mathcal{P}_4)$ is dense and countable. In this work, we willcalculate explicitly the degree of the rational first integral of thefoliations in this linear family, as a function of the parameter.

Degree of the First Integral of a Foliation in the Pencil $\mathcal{P}_4$