By analyzing 2.93 fb$^{-1}$ of data collected at $sqrt s=3.773$ GeV with the BESIII detector, we measure the absolute branching fraction ${mathcal B}(D^{+}rightarrowbar K^0mu^{+} u_{mu})=(8.72 pm 0.07_{rm stat.} pm 0.18_{rm sys.})%$, which is consistent with previous measurements within uncertainties but with significantly improved precision. Combining the Particle Data Group values of ${mathcal B}(D^0to K^-mu^+ u_mu)$, ${mathcal B}(D^{+}rightarrowbar K^0 e^{+} u_{e})$, and the lifetimes of the $D^0$ and $D^+$ mesons with the value of ${mathcal B}(D^{+}rightarrowbar K^0 mu^{+} u_{mu})$ measured in this work, we determine the following ratios of partial widths: $Gamma(D^0to K^-mu^+ u_mu)/Gamma(D^{+}rightarrowbar K^0mu^{+} u_{mu})=0.963pm0.044$ and $Gamma(D^{+}rightarrowbar K^0 mu^{+} u_{mu})/Gamma(D^{+}rightarrowbar K^0 e^{+} u_{e})=0.988pm0.033$.
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