2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139867We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values on open sets is obtained. We illustrate our approach on some problems taken from the literature. An alternative proof of the integrability of the sub-Riemannian nilpotent Lie group of type (2,3,5) is also given.Presented at the 4th Junior European Meeting on "Control and Optimization", Bialystok Technical University, Bialystok, Poland, 11-14 September 2005Optimization and Control49K15; 70H33; 37J15text