  The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems
were introduced in an ad hoc fashion rather than being derived from the
solution of the inverse problem of variational calculus. We begin with the
first integral of the equation of motion and solve the associated inverse
problem to obtain some of the existing results for NSLs. In addition, we
provide a number of alternative Lagrangian representations. The case studies
envisaged by us include (i) the usual modified Emden-type equation, (ii)
Emden-type equation with dissipative term quadratic in velocity and (iii)
Lokta-Volterra model. We point out that our method is quite general for
applications to other physical systems.
