Measurements of inclusive differential cross sections for charged pion and kaon production in e(+)e(-) annihilation have been carried out at a center-of-mass energy of root s = 10.52 GeV. The measurements were performed with the Belle detector at the KEKB e(+)e(-) collider using a data sample containing 113 X 10(6) e(+)e(-) -> q (q) over bar events, where q = {u, d, s, c}. We present charge-integrated differential cross sections d sigma(h+)/dz for h(+/-) = {pi(+/-), K-+/-} as a function of the relative hadron energy z = 2E(h)/root s from 0.2 to 0.98. The combined statistical and systematic uncertainties for pi(+/-) (K-+/-) are 4% (4%) at z similar to 0.6 and 15% (24%) at z similar to 0.9. The cross sections are the first measurements of the z dependence of pion and kaon production for z > 0.7 as well as the first precision cross section measurements at a center-of-mass energy far below the Z(0) resonance used by the experiments at LEP and SLC.