Inclusive semileptonic B_s^0 -> X^+ l^- u decays are studied for the first time using a 23.6 fb^{-1} data sample collected on the Y(5S) resonance with the Belle detector at the KEKB asymmetric energy e^+ e^- collider. These decays are identified by the means of a lepton accompanied by a same-sign D_s^+ meson originating from the other B_s^0 in the event. The semileptonic branching fractions are measured in the electron and muon channels to be Bf(B_s^0 -> X^+ e^- u) = (10.9 pm 1.0 pm 0.9)% and Bf(B_s^0 -> X^+ mu^- u) = (9.2 pm 1.0 pm 0.8)%, respectively. Assuming an equal electron and muon production rate in B_s^0 decays, a combined fit yields an average leptonic branching fraction Bf(B_s^0 -> X^+ l^- u) = (10.2 pm 0.8 pm 0.9)%.
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