See paper for full list of authors - 12 pages plus author list (26 pages total), 5 figures, 5 tablesThis Letter reports on a first measurement of the inclusive W+jets cross section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC, with the ATLAS detector. Cross sections, in both the electron and muon decay modes of the W boson, are presented as a function of jet multiplicity and of the transverse momentum of the leading and next-to-leading jets in the event. Measurements are also presented of the ratio of cross sections sigma(W+ \ge n) / sigma(W+ \ge n-1) for inclusive jet multiplicities n=1-4. The results, based on an integrated luminosity of 1.3 pb-1, have been corrected for all known detector effects and are quoted in a limited and well-defined range of jet and lepton kinematics. The measured cross sections are compared to particle-level predictions based on perturbative QCD. Next-to-leading order calculations, studied here for n \le 2, are found in good agreement with the data. Leading-order multiparton event generators, normalized to the NNLO total cross section, describe the data well for all measured jet multiplicities
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