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The ALICE Collaboration at the LHC reports measurement of the inclusive production cross section of electrons from semi-leptonic decays of beauty hadrons with rapidity |y| < 0.8 and transverse momentum 1 < pT < 10 GeV/c, in pp collisions at √s = 2.76 TeV. Electrons not originating from semi-electronic decay of beauty hadrons are suppressed using the impact parameter of the corresponding tracks. The production cross section of beauty decay electrons is compared to the result obtained with an alternative method which uses the distribution of the azimuthal angle between heavy-flavour decay electrons and charged hadrons. Perturbative QCD predictions agree with the measured cross section within the experimental and theoretical uncertainties. The integrated visible cross section, σb→e = 3.47 ± 0.40(stat) +1.12 −1.33(sys) ± 0.07(norm) μb, was extrapolated to full phase space using Fixed Order plus Next-to-Leading Log (FONLL) calculations to obtain the total bb production ¯ cross section, σbb¯ = 130 ± 15.1(stat) +42.1 −49.8(sys) +3.4 −3.1(extr) ± 2.5(norm) ± 4.4(BR) μb.