  We perform a detailed study on the integrability of the Ho\v{r}% ava-Lifshitz
scalar field cosmology in a Friedmann--Lema\^{\i}% tre--Robertson--Walker
background spacetime. The approach we follow to determine the integrability is
that of the Singularity Analysis. More specifically, we test if the
gravitational field equations possesses the Painlev\'{e} property. For the
exponential potential of the scalar field we are able to perform an analytic
explicit integration of the field equations and write the solution in terms of
Laurent expansion and more specifically write the solution in terms of Right
Painlev\'{e} series.
