  We consider a Markov process $X$ associated to a nonnecessarily symmetric
Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a
class of additive functionals of zero quadratic variation and then we obtain an
It\^{o} formula for the process $u(X)$, when $u$ is locally in the domain of
$\mathcal{E}$.
