First integrals for a generalized coupled Lane–Emden system

We classify a generalized coupled Lane–Emden system tü+nu̇+tf(t)vq=0,tv̈+nv̇+tf(t)up=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries it admits. First integrals of the various cases which admit Noether point symmetries are then obtained for the generalized coupled Lane–Emden system under consideration.