We present a measurement of the inclusive top quark pair production cross section in \ppbar collisions at (\sqrt{s}=1.96) TeV utilizing data corresponding to an integrated luminosity of \lumi\ collected with the D0 detector at the Fermilab Tevatron Collider. We consider final states containing one high-$p_{T}$ isolated electron or muon and at least two jets, and we perform three analyses: one exploiting specific kinematic features of \ttbar events, the second using $b$-jet identification, and the third using both techniques to separate \ttbar\ signal from background. In the third case, we determine simultaneously the $t\bar{t}$ cross section and the ratio of the production rates of $W$+heavy flavor jets and $W$+light flavor jets, which reduces the impact of the systematic uncertainties related to the background estimation. Assuming a top quark mass of 172.5 GeV, we obtain $\sigma_{t\bar{t}} = 7.78^{+0.77}_{-0.64} $ pb. This result agrees with predictions of the standard model.