We present an algorithm to study the local behavior of singular points of planar analytic vector fields having a first integral which is a quotient of analytic functions. The algorithm is based on the blow-up method. It emphasizes the curves passing through the singular points and avoids the computation of the desingularized systems. Vector fields having a rational first integral are a particular case.
Álvarez, M.; Ferragut, A. Local behavior of planar analytic vector fields via integrability. "Analysis and applications", Gener 2012, vol. 385, núm. 1, p. 264-277.