Charm production at the LHC in pp collisions at s=7TeV is studied with the LHCb detector. The decays D0→K-π+, D+→K-π+π+, D*+→D0(K-π+)π+, Ds+→φ(K-K+)π+, Λc+→pK-π+, and their charge conjugates are analysed in a data set corresponding to an integrated luminosity of 15 nb-1. Differential cross-sections dσ/dpT are measured for prompt production of the five charmed hadron species in bins of transverse momentum and rapidity in the region 0<pT<8GeV/c and 2.0<y<4.5. Theoretical predictions are compared to the measured differential cross-sections. The integrated cross-sections of the charm hadrons are computed in the above pT-y range, and their ratios are reported. A combination of the five integrated cross-section measurements givesσ(cc̄)pT<8GeV/c,2.0<y<4.5=1419±12(stat)±116(syst)±65(frag)μb, where the uncertainties are statistical, systematic, and due to the fragmentation functions. © 2013 CERN.