The total cross section and differential cross sections for the production of B-c(+/-) mesons, times their branching fraction to J/psi pi(+/-), are measured relative to those for the production of B-+/- mesons, times their branching fraction to J/psi K-+/-. The data used for this study correspond to an integrated luminosity of 20.3 fb(-1) of pp collisions recorded by the ATLAS detector at the Large Hadron Collider in 2012 at a center-of-mass energy of root s = 8 TeV. The measurement is performed differentially in bins of transverse momentum p(T) for 13 GeV < p(T)(B-c(+/-)) < 22 GeV and p(T)(B-c(+/-)) > 22 GeV and in bins of rapidity y for vertical bar y vertical bar < 0.75 and 0.75 < vertical bar y vertical bar < 2.3. The relative cross section times branching fraction for the full range p(T) > 13 GeV and vertical bar y vertical bar < 2.3 is (0.34 +/- 0.04(stat) (+0.06)(-0.02 sys) +/- 0.01(lifetime))%. The differential measurements suggest that the production cross section of the B-c(+/-) decreases faster with p(T) than the production cross section of the B-+/-, while no significant dependence on rapidity is observed.