We present statistically significant detections at 850um of the Lyman Break Galaxy (LBG) population at z=3, 4, and 5 using data from the Submillimetre Common User Bolometer Array 2 (SCUBA-2) Cosmology Legacy Survey (S2CLS) in the United Kingdom Infrared Deep Sky Survey Ultra Deep Survey (UKIDSS-UDS) field. We employ a stacking technique to probe beneath the survey limit to measure the average 850um flux density of LBGs at z=3, 4, and 5 with typical ultraviolet luminosities of L(1700A)~10^29 erg/s/Hz. We measure 850um flux densities of (0.25 +/- 0.03, (0.41 +/- 0.06), and (0.88 +/- 0.23) mJy respectively, and find that they contribute at most 20 per cent to the cosmic far-infrared background at 850um. Fitting an appropriate range of spectral energy distributions to the z=3, 4, and 5 LBG stacked 24-850um fluxes, we derive infrared (IR) luminosities of L(8-1000um)~3.2, 5.5, and 11.0x10^11 Lsun (corresponding to star formation rates of ~50-200 Msun/yr) respectively. We find that the evolution in the IR luminosity density of LBGs is broadly consistent with model predictions for the expected contribution of luminous IR galaxy (LIRG) to ultraluminous IR galaxy (ULIRG) type systems at these epochs. We also see a strong positive correlation between stellar mass and IR luminosity. Our data are consistent with the main sequence of star formation showing little or no evolution from z=3 to 5. We have also confirmed that, for a fixed mass, the reddest LBGs (UV slope Beta -> 0) are indeed redder due to dust extinction, with SFR(IR)/SFR(UV) increasing by approximately an order of magnitude over -2<Beta<0 such that SFR(IR)/SFR(UV)~20 for the reddest LBGs. Furthermore, the most massive LBGs also tend to have higher obscured-to-unobscured ratio, hinting at a variation in the obscuration properties across the mass range.
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