We present a fully non-perturbative computation of the inclusive semileptonic $D_s \to X \ell \nu$ decay and its leptonic moments from lattice QCD.
A first principles computation of such observables has a phenomenological relevance since its comparison with experimental data allows for stringent Standard Model tests in the sector of Flavour physics.
Additionally, this work sets the stage to a future project involving the B meson(s).
The computation, performed employing state-of-the-art ETMC ensembles at the physical point with four lattice spacings and three volumes, is carried out by extracting smeared spectral densities from Euclidean four-point correlation functions.
In this talk, we introduce the HLT method used for extracting spectral densities and present results of the calculations as well as the error analysis.