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We present a search for direct CP violation in B±→J/ψK±(π±) decays. The event sample is selected from 2.8 fb-1 of pp collisions recorded by D0 experiment in run II of the Fermilab Tevatron Collider. The charge asymmetry ACP(B+→J/ψK+) =+0.0075 ±± 0.0061(stat) ± 0.0030(syst) is obtained using a sample of approximately 40 000 B±→J/ψK±decays. The achieved precision is of the same level as the expected deviation predicted by some extensions of the standard model. We also measured the charge asymmetry ACP(B+→J/ψK+) = -0.09 ± 0.08(stat) ± 0.03(syst).