Total J/psi production cross section at the LHC

We evaluate the production cross section for direct J/psi integrated in P_T for various collision energies of the LHC in the QCD-based Colour-Singlet Model. We consider the LO contribution from gluon fusion as well as the one from a fusion of a gluon and a charm quark from the colliding protons. The rapidity distribution of the yield is evaluated in the central region relevant for the ATLAS and CMS detectors, as well as in the more forward region relevant for the ALICE and LHC-b detectors. The results obtained here are compatible with those of other approaches within the range of the theoretical uncertainties which are admittedly very large. This suggests that the "mere" measurements of the yield at the LHC will not help disentangle between the different possible quarkonium production mechanisms.