The production of the X(3872) is studied in pp collisions at s√=7 TeV, using decays to J/ψπ + π −, where the J/ψ decays to two muons. The data were recorded by the CMS experiment and correspond to an integrated luminosity of 4.8 fb−1. The measurements are performed in a kinematic range in which the X(3872) candidates have a transverse momentum 10 < p T < 50 GeV and rapidity |y| < 1.2. The ratio of the X(3872) and ψ(2S) cross sections times their branching fractions into J/ψπ + π − is measured as a function of p T. In addition, the fraction of X(3872) originating from B decays is determined. From these measurements the prompt X(3872) differential cross section times branching fraction as a function of p T is extracted. The π + π − mass spectrum of the J/ψπ + π − system in the X(3872) decays is also investigated.