  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,
$^{40}$Ar($\nu_\mu$,$\mu$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.
