Measurement of the $J/\psi$ inclusive production cross-section in pp collisions at $\sqrt{s}=7TeV$ with ALICE at the LHC

ALICE measures the J/psi production at mid-rapidity (|y| < 0.9) in the di-electron decay channel as well as at forward rapidity (2.5 < y < 4.0) in the di-muon decay channel. In both channels the acceptance goes down to zero transverse momentum. We present the rapidity dependence of the inclusive J/psi production cross-section and transverse momentum spectra.