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The inclusive cross section for J/ψ production times the branching ratio B(J/ψ→μ+μ-) has been measured in the forward pseudorapidity region: B×dσ[p̅+p→J/ψ(pT>10 GeV/c,2.1<|η|<2.6)+X]/dη=192±9(stat)±29(syst) pb. The results are based on 74.1±5.2 pb-1 of data collected by the CDF Collaboration at the Fermilab Tevatron Collider. The measurements extend earlier measurements of the D0 Collaboration to higher pTJ/ψ. In the kinematic range where the experiments partially overlap, these data are in good agreement with previous measurements.