  Here we present a method to find elementary first integrals of rational
second order ordinary differential equations (SOODEs) based on a Darboux type
procedure \cite{ManMac,firsTHEOps1,secondTHEOps1}. Apart from practical
computational considerations, the method will be capable of telling us (up to a
certain polynomial degree) if the SOODE has an elementary first integral and,
in positive case, finds it via quadratures.
