%0 Journal Article %T A class of polynomial planar vector fields with polynomial first integral %A A. Ferragut %A C. Galindo %A F. Monserrat %J Mathematics %D 2014 %I arXiv %X We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral. In addition, we solve the Poincar\'e problem for the class of systems which admit a polynomial first integral as above in the sense that the degree of the minimal first integral can be computed from the reduction of singularities of the corresponding vector field. %U http://arxiv.org/abs/1410.3652v1