We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element vertical bar V(cb)vertical bar based on a sample of about 53 700 (B) over bar (0) -> D*(+)l(-)(nu) over bar (l) decays observed by the BABAR detector. We obtain the branching fraction averaged over l = e, mu, B((B) over bar (0) -> D*(+)l(-)(nu) over bar (l)) = (4.90 +/- 0.07(stat.)(-0.35)(+0.36)(syst.))%. We measure the differential decay rate as a function of iv, the relativistic boost gamma of the D*+ in the Wo rest frame. By extrapolating d Gamma/dw to the kinematic limit w -> 1, we extract the product of vertical bar V(cb)vertical bar and the axial form factor A(1)(w = 1). We combine this measurement with a lattice QCD calculation of A(1)(w = 1) to determine vertical bar V(cb)vertical bar = (38.7 +/- 0.3(stat.) +/- 1.7(syst.)(-1.3)(+1.5)(theory)) x 10(-3).
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