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We report on the first measurement of flux-integrated single differential cross sections for charged-current (CC) muon neutrino ($\nu_{\mu}$) scattering on argon with a muon and a proton in the final state, 40Ar $(\nu_{\mu},μp)X$. The measurement was carried out using the Booster Neutrino Beam at Fermi National Accelerator Laboratory and the MicroBooNE liquid argon time projection chamber detector with an exposure of 4.59 × 1019 protons on target. Events are selected to enhance the contribution of CC quasielastic (CCQE) interactions. The data are reported in terms of a total cross section as well as single differential cross sections in final state muon and proton kinematics. We measure the integrated per-nucleus CCQE-like cross section (i.e., for interactions leading to a muon, one proton, and no pions above detection threshold) of (4.93 ± 0.76stat ± 1.29sys)×10-38 cm2, in good agreement with theoretical calculations. The single differential cross sections are also in overall good agreement with theoretical predictions, except at very forward muon scattering angles that correspond to low-momentum-transfer events.