  We study integrability by quadrature of a spatially flat Friedmann model
containing both a minimally coupled scalar field $\phi$ with an exponential
potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi
G_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state
$p=(1-h)\rho$. From the mathematical view point the model is pseudo-Euclidean
Toda-like system with 2 degrees of freedom. We apply the methods developed in
our previous papers, based on the Minkowsky-like geometry for 2 characteristic
vectors depending on the parameters $\sigma$ and $h$. In general case the
problem is reduced to integrability of a second order ordinary differential
equation known as the generalized Emden-Fowler equation, which was investigated
by discrete-group methods. We present 4 classes of general solutions for the
parameters obeying the following relations: {\bf A}. $\sigma$ is arbitrary,
$h=0$; {\bf B}. $\sigma=1-h/2$, $0<h<2$; {\bf C1}. $\sigma=1-h/4$, $0<h\leq 2$;
{\bf C2}. $\sigma=|1-h|$, $0<h\leq 2$, $h\neq 1,4/3$. We discuss the properties
of the exact solutions near the initial singularity and at the final stage of
evolution.
