  We calculate the average single particle density of states in graphene with
disorder due to impurity potentials. For unscreened short-ranged impurities, we
use the non-self-consistent and self-consistent Born and $T$-matrix
approximations to obtain the self-energy. Among these, only the self-consistent
$T$-matrix approximation gives a non-zero density of states at the Dirac point.
The density of states at the Dirac point is non-analytic in the impurity
potential. For screened short-ranged and charged long-range impurity
potentials, the density of states near the Dirac point typically increases in
the presence of impurities, compared to that of the pure system.
