The branching fractions of the decays $B^{+} to eta ell^{+} u_{ell}$ and $B^{+} to eta^{prime} ell^{+} u_{ell}$ are measured, where $ell$ is either an electron or a muon, using a data sample of $711,{rm fb}^{-1}$ containing $772 times 10^6 Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. To reduce the dependence of the result on the form factor model, the measurement is performed over the entire $q^2$ range. The resulting branching fractions are ${cal B}(B^{+} rightarrow eta ell^{+} u_{ell}) = (2.83 pm 0.55_{rm (stat.)} pm 0.34_{rm (syst.)}) times 10^{-5}$ and ${cal B}(B^{+} rightarrow eta ell^{+} u_{ell}) = (2.79 pm 1.29_{rm (stat.)} pm 0.30_{rm (syst.)}) times 10^{-5}$.
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