  Given a real- or complex-analytic singular foliation $\theta$ with $n$ first
integrals of meromorphic or Darboux type $(f_1,\dots,f_n)$, we prove that there
exists a local monomialization of the first integrals. In particular, if
$\theta$ is generated by the $n$ first integrals, we prove the existence of a
local reduction of singularities of $\theta$ to monomial singularities.
