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By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV with By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the 𝐷+→𝜂𝜇+𝜈𝜇 decay to be ℬ𝐷+→𝜂𝜇+𝜈𝜇=(10.4±1.0stat±0.5syst)×10−4. Using the world averaged value of ℬ𝐷+→𝜂𝑒+𝜈𝑒, the ratio of the two branching fractions is determined to be ℬ𝐷+→𝜂𝜇+𝜈𝜇/ℬ𝐷+→𝜂𝑒+𝜈𝑒=0.91±0.13(stat+syst), which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain the product of the hadronic form factor 𝑓𝜂+(0) and the 𝑐→𝑑 Cabibbo-Kobayashi-Maskawa matrix element |𝑉𝑐𝑑| to be 𝑓𝜂+(0)|𝑉𝑐𝑑|=0.087±0.008stat±0.002syst. Taking the input of |𝑉𝑐𝑑| from the global fit in the standard model, we determine 𝑓𝜂+(0)=0.39±0.04stat±0.01syst. On the other hand, using the value of 𝑓𝜂+(0) calculated in theory, we find |𝑉𝑐𝑑| = 0.242±0.022stat±0.006syst±0.033theory.