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

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