We report on the first measurement of flux-integrated single differential cross sections for charged-current (CC) muon neutrino ($ u_mu$) scattering on argon with a muon and a proton in the final state, $^{40}$Ar($ u_mu$,$mu$p)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 $times$ 10$^{19}$ 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 $pm$ 0.76stat $pm$ 1.29sys) $times$ 10$^{-38}$cm$^2$, 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.
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