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Using 482~pb$^{-1}$ of $e^+e^-$ collision data collected at a center-of-massenergy of $\sqrt{s} = 4.009$ GeV with the BESIII detector, we measure thebranching fractions of the decays $D_s^+\to\mu^+\nu_\mu$ and$D_s^+\to\tau^+\nu_\tau$. By constraining the ratio of decay rates of $D_s^+$to $\tau^+\nu_\tau$ and to $\mu^+\nu_\mu$ to the Standard Model prediction, thebranching fractions are determined to be $\mathcal{B}(D_s^+ \to \mu^+\nu_\mu) =(0.495 \pm 0.067 \pm 0.026)\%$ and $\mathcal{B}(D_s^+ \to \tau^+\nu_\tau) =(4.83 \pm 0.65 \pm 0.26)\%$. Using these branching fractions, we obtain a valuefor the decay constant $f_{D_s^+}$ of $(241.0 \pm 16.3 \pm 6.5)~\text{MeV}$,where the first error is statistical and the second systematic.

Measurement of the $D_s^+ \to \ell^+\nu_\ell$ branching fractions and the decay constant $f_{D_s^+}$