In this paper we complete a research effected in a Memoir of the Academy of Sciences of Turin and in a Note of the Venetian Institute in the year 1937, concerning the determination of all types of kinetic energy and potential of forces which make integrable by separation of variables the corresponding dynamical equation of Hamilton-Jacobi. We show that this equation is in effect soluble by separation of variables and we assign the corresponding complete integrals in the general case.