A measurement of the $CP$ asymmetry in $B^+ rightarrow K^+ mu^+ mu^-$ decays is presented using $pp$ collision data, corresponding to an integrated luminosity of 1.0${,fb}^{-1}$, recorded by the LHCb experiment during 2011 at a centre-of-mass energy of 7 TeV. The measurement is performed in seven bins of $mu^+ mu^-$ invariant mass squared in the range ${0.05<q^{2}<22.00{mathrm{GeV^2/}c^4}}$, excluding the ${J/psi}$ and $psi{(2S)}$ resonance regions. Production and detection asymmetries are corrected for using the $B^+ rightarrow J/psi K^+$ decay as a control mode. Averaged over all the bins, the $CP$ asymmetry is found to be ${{cal A}_{CP} = 0.000pm 0.033{(stat.)} pm0.005 {(syst.)} pm 0.007{}(J/psi K^+)}$, where the third uncertainty is due to the $CP$ asymmetry of the control mode. This is consistent with the Standard Model prediction.
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