  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.
