  We consider one-dimensional exclusion processes with long jumps given by a
transition probability of the form $p_n(\cdot)=s(\cdot)+\gamma_na(\cdot)$, such
that its symmetric part $s(\cdot)$ is irreducible with finite variance and its
antisymmetric part is absolutely bounded by $s(\cdot).$ We prove that under
diffusive time scaling and strength of asymmetry $\sqrt n \gamma_n
\to_{n\to\infty} b\neq 0$, the equilibrium density fluctuations are given by
the unique energy solution of the stochastic Burgers equation.
