Extension de la torsion analytique holomorphe aux fibr\'es en droites int\'egrables

Let $X$ be a compact K"ahler manifold. We extend the notion of Quillen metric to the set of integrable line bundles on $X$. In particular, we prove that the notion of holomorphic analytic torsion extends to integrable line bundles $\bar{L}$, such that $H^q(X,L)=0$ for $q\ge 1$.