We present a linear clustering model of cosmic infrared background (CIB) anisotropies at large scales that is used to measure the cosmic star formation rate density up to redshift 6, the effective bias of the CIB and the mass of dark-matter halos hosting dusty star-forming galaxies. This is achieved using the Planck CIB auto- and cross-power spectra (between different frequencies) and CIBxCMB lensing cross-spectra measurements, as well as external constraints (e.g. on the CIB mean brightness). We recovered an obscured star formation history which agrees well with the values derived from infrared deep surveys and we confirm that the obscured star formation dominates the unobscured one up to at least z=4. The obscured and unobscured star formation rate densities are compatible at $1sigma$ at z=5. We also determined the evolution of the effective bias of the galaxies emitting the CIB and found a rapid increase from $sim$0.8 at z$=$0 to $sim$8 at z$=$4. At 2$<$z$<$4, this effective bias is similar to that of galaxies at the knee of the mass functions and submillimeter galaxies. This effective bias is the weighted average of the true bias with the corresponding emissivity of the galaxies. The halo mass corresponding to this bias is thus not exactly the mass contributing the most to the star formation density. Correcting for this, we obtained a value of log(M$_h$/M$_{odot}$)=12.77$_{-0.125}^{+0.128}$ for the mass of the typical dark matter halo contributing to the CIB at z=2. Finally, we also computed using a Fisher matrix analysis how the uncertainties on the cosmological parameters affect the recovered CIB model parameters and find that the effect is negligible.
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