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We report on measurements of differential cross sections d /dpT for prompt charm meson production in pp̅ collisions at √s=1.96 TeV using 5.8±0.3 pb-1 of data from the CDF II detector at the Fermilab Tevatron. The data are collected with a new trigger that is sensitive to the long lifetime of hadrons containing heavy flavor. The charm meson cross sections are measured in the central rapidity region |y|≤1 in four fully reconstructed decay modes: D0→K- π+, D*+→D0 π+, D+→K- π+ π+, Ds+→ Φπ+, and their charge conjugates. The measured cross sections are compared to theoretical calculations.