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We report new measurements of the branching fraction ℬ(𝐷+𝑠→ℓ+𝜈), where ℓ+ is either 𝜇+ or 𝜏+(→𝜋+¯𝜈𝜏), based on 6.32 fb−1 of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating the 𝐷+𝑠→𝜇+𝜈𝜇 and 𝐷+𝑠→𝜏+𝜈𝜏 components yields ℬ(𝐷+𝑠→𝜏+𝜈𝜏)=(5.21±0.25±0.17)×10−2, ℬ(𝐷+𝑠→𝜇+𝜈𝜇)=(5.35±0.13±0.16)×10−3, and the ratio of decay widths 𝑅=Γ(𝐷+𝑠→𝜏+𝜈𝜏)Γ(𝐷+𝑠→𝜇+𝜈𝜇)=9.73+0.61−0.58±0.36, where the first uncertainties are statistical and the second systematic. No evidence of 𝐶𝑃 asymmetry is observed in the decay rates 𝐷±𝑠→𝜇±𝜈𝜇 and 𝐷±𝑠→𝜏±𝜈𝜏: 𝐴𝐶𝑃(𝜇±𝜈)=(−1.2±2.5±1.0)% and 𝐴𝐶𝑃(𝜏±𝜈)=(+2.9±4.8±1.0)%. Constraining our measurement to the Standard Model expectation of lepton universality (𝑅=9.75), we find the more precise results ℬ(𝐷+𝑠→𝜏+𝜈𝜏)=(5.22±0.10±0.14)×10−2 and 𝐴𝐶𝑃(𝜏±𝜈𝜏)=(−0.1±1.9±1.0)%. Combining our results with inputs external to our analysis, we determine the 𝑐→¯𝑠 quark mixing matrix element, 𝐷+𝑠 decay constant, and ratio of the decay constants to be |𝑉𝑐𝑠|=0.973±0.009±0.014, 𝑓𝐷+𝑠=249.9±2.4±3.5 MeV, and 𝑓𝐷+𝑠/𝑓𝐷+=1.232±0.035, respectively.