Differential cross sections are presented for the prompt and non-prompt production of the hidden-charm state $X(3872)$ and $\psi(2S)$, in the decay mode $J/\psi\pi^+\pi^-$, measured at $\sqrt{s} = 8$ TeV by the ATLAS detector at LHC. In the non-prompt production, the data suggest the presence of a short-lived component, which may be due to $B_c$ decays. The dipion invariant masses in both $X(3872)$ and $\psi(2S)$ are measured and compared to theoretical predictions.