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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,3,30]]},"abstract":"<jats:p> In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane [Formula: see text]. The criterion uses solutions of the form [Formula: see text] of the differential system in the plane and their associated cofactors, where [Formula: see text] is a formal power series. In particular, the criterion provides the necessary conditions in order that some polynomial differential systems in [Formula: see text] would be formal Weierstrass integrable. Inside this class there exist non-Liouvillian integrable systems. 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