  We use the Bethe Ansatz to derive analytical expressions for the current
statistics in the asymmetric exclusion process with both forward and backward
jumps. The Bethe equations are highly coupled and this fact has impeded their
use to derive exact results for finite systems. We overcome this technical
difficulty by a reformulation of the Bethe equations into a one variable
polynomial problem, akin to the functional Bethe Ansatz. The perturbative
solution of this equation leads to the cumulants of the current. We calculate
here the first two orders and derive exact formulae for the mean value of the
current and its fluctuations.
