Measurement of branching fractions and charge asymmetries in B+ decays to eta pi(+), eta K+, eta rho(+), and eta(')pi(+), and search for B-0 decays to eta K-0 and eta omega

We present measurements of branching fractions and charge asymmetries for six B-meson decay modes with an eta or eta' meson in the final state. The data sample corresponds to 232 x 10(6) BB pairs collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) B Factory at SLAC. We measure the branching fractions (in units of 10(-6)): B(B+ -> eta pi(+)) = 5.1 +/- 0.6 +/- 0.3, B(B+ -> eta K+) = 3.3 +/- 0.6 +/- 0.3, B(B-0 -> eta K-0) = 1.5 +/- 0.7 +/- 0.1 (< 2.5 at 90% C.L.), B(B+ -> eta rho(+)) = 8.4 +/- 1.9 +/- 1.1, B(B-0 -> eta omega) = 1.0 +/- 0.5 +/- 0.2 (< 1.9 at 90% C.L.), and B(B+ -> eta'pi(+)) = 4.0 +/- 0.8 +/- 0.4, where the first uncertainty is statistical and second systematic. For the charged modes we also determine the charge asymmetries, all found to be compatible with zero.