Differential cross sections are presented for the prompt and non-prompt production of the hidden-charm states X (3872) and ψ (2 S ), in the decay mode J/ψπ + π − , measured using 11.4 fb −1 of pp collisions at √s = 8 TeV by the ATLAS detector at the LHC. The ratio of cross-sections X (3872) /ψ (2 S ) is also given, separately for prompt and non-prompt components, as well as the non-prompt fractions of X (3872) and ψ (2 S ). Assuming independent single effective lifetimes for non-prompt X (3872) and ψ (2 S ) production gives R B = ℬ B → X 3872 + any ℬ X 3872 → J / ψ π + π − ℬ B → ψ 2 S + any ℬ ψ 2 S → J / ψ π + π − = 3.95 ± 0.32 stat ± 0.08 s y s × 10 − 2 $$ {R}_B=\frac{\mathrm{\mathcal{B}}\left(B\to X(3872)+\mathrm{any}\right)\mathrm{\mathcal{B}}\left(X(3872)\to J/\psi {\pi}^{+}{\pi}^{-}\right)}{\mathrm{\mathcal{B}}\left(B\to \psi (2S)+\mathrm{any}\right)\mathrm{\mathcal{B}}\left(\psi (2S)\to J/\psi {\pi}^{+}{\pi}^{-}\right)}=\left(3.95\pm 0.32\left(\mathrm{s}\mathrm{tat}\right)\pm 0.08\left(\mathrm{s}\mathrm{y}\mathrm{s}\right)\right)\times {10}^{-2} $$ separating short- and long-lived contributions, assuming that the short-lived component is due to B c decays, gives R B = (3 . 57 ± 0 . 33(stat) ± 0 . 11(sys)) × 10 −2 , with the fraction of non-prompt X (3872) produced via B c decays for p T ( X (3872)) > 10 GeV being (25 ± 13(stat) ± 2(sys) ± 5(spin))%. The distributions of the dipion invariant mass in the X (3872) and ψ (2 S ) decays are also measured and compared to theoretical predictions.