Abstract: We describe a measurement of the ratio of the cross sections times branching fractions of the B+c meson in the decay mode B+c?J/?µ+? to the B+ meson in the decay mode B+?J/?K+ in proton-antiproton collisions at center-of-mass energy vs=1.96??TeV. The measurement is based on the complete CDF Run II data set, which comes from an integrated luminosity of 8.7??fb-1. The ratio of the production cross sections times branching fractions for B+c and B+ mesons with momentum transverse to the beam greater than 6??GeV/c and rapidity magnitude smaller than 0.6 is 0.211±0.012(stat)+0.021-0.020(syst). Using the known B+?J/?K+ branching fraction, the known B+ production cross section, and a selection of the predicted B+c?J/?µ+?branching fractions, the range for the total B+c production cross section is estimated.

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