The differential cross section and charge asymmetry for inclusive $\mathrm {p}\mathrm {p}\rightarrow \mathrm {W}^{\pm }+X \rightarrow \mu ^{\pm }\nu +X$ production at $\sqrt{s}=8,\mathrm{TeV} $ are measured as a function of muon pseudorapidity. The data sample corresponds to an integrated luminosity of 18.8 $,\text {fb}^{-1}$ recorded with the CMS detector at the LHC. These results provide important constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable x from $10^{-3}$ to $10^{-1}$ .