ABSTRACT We investigate the relation between active galactic nucleus (AGN) and star formation (SF) activity at 0.5 < z < 3 by analysing 898 galaxies with X-ray luminous AGNs (LX > 1044 erg s−1) and a large comparison sample of ∼320 000 galaxies without X-ray luminous AGNs. Our samples are selected from a large (11.8 deg2) area in Stripe 82 that has multiwavelength (X-ray to far-IR) data. The enormous comoving volume (∼0.3 Gpc3) at 0.5 < z < 3 minimizes the effects of cosmic variance and captures a large number of massive galaxies (∼30 000 galaxies with M* > 1011 M⊙) and X-ray luminous AGNs. While many galaxy studies discard AGN hosts, we fit the SED of galaxies with and without X-ray luminous AGNs with Code Investigating GALaxy Emission and include AGN emission templates. We find that without this inclusion, stellar masses and star formation rates (SFRs) in AGN host galaxies can be overestimated, on average, by factors of up to ∼5 and ∼10, respectively. The average SFR of galaxies with X-ray luminous AGNs is higher by a factor of ∼3–10 compared to galaxies without X-ray luminous AGNs at fixed stellar mass and redshift, suggesting that high SFRs and high AGN X-ray luminosities may be fuelled by common mechanisms. The vast majority ($\gt 95 {{\ \rm per\ cent}}$) of galaxies with X-ray luminous AGNs at z = 0.5−3 do not show quenched SF: this suggests that if AGN feedback quenches SF, the associated quenching process takes a significant time to act and the quenched phase sets in after the highly luminous phases of AGN activity.