We present measurements of production cross sections of single top quarks in $\ppbar$ collisions at $\sqrt{s}=1.96\;\rm TeV$ in a data sample corresponding to an integrated luminosity of $5.4\;\rm fb^{-1}$ collected by the D0 detector at the Fermilab Tevatron Collider. We select events with an isolated electron or muon, an imbalance in transverse energy, and two, three, or four jets, with one or two of them containing a bottom hadron. We obtain an inclusive cross section of $\sigma({\ppbar}{\rargap}tb+X, tqb+X) = 3.43\pm^{0.73}_{0.74}\;\rm pb$ and use it to extract the CKM matrix element $0.79 < |V_{tb}| \leq 1$ at the 95% C.L. We also measure $\sigma({\ppbar}{\rargap}tb+X) = 0.68\pm^{0.38}_{0.35}\;\rm pb$ and $\sigma({\ppbar}{\rargap}tqb+X) = 2.86\pm^{0.69}_{0.63}\;\rm pb$ when assuming, respectively, $tqb$ and $tb$ production rates as predicted by the standard model.