We present a new effcient method for finding special integrals of ODEs. Special integrals are used to find special exact solutions (e.g. rational and elementary solutions).

As a nontrivial application it is shown that there exist special integrals y of the Painleve equation diff(y,x$2) = 2y^3 +xy + alpha if and only if alpha = (2m + 1)/2.