  The Prelle-Singer method allows determining an elementary first integral
admitted by a polynomial vector field in the plane. It is a semi-algorithm
whose nonlinear step consists of determining the Darboux polynomials of the
vector field. In this article we construct a linear procedure to determine the
Darboux polynomials present in the integrating factor of a polynomial vector
field in the plane. Next, we extend the procedure to deal with rational 2ODEs
that admit an elementary first integral
