A search is presented for the standard model Higgs boson produced in association with top quarks using the full Run II proton-antiproton collision data set, corresponding to 9.45 inverse fb, collected by the Collider Detector at Fermilab. No significant excess over the expected background is observed, and 95% credibility-level upper bounds are placed on the cross section sigma(t\bar{t}H --> lepton + missing transverse energy + jets). For a Higgs boson mass of 125 GeV, we expect to set a limit of 12.6, and observe a limit of 20.5 times the standard model rate. This represents the most sensitive search for a standard model Higgs boson in this channel to date.

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