SN 2010jl: Optical to hard X-ray observations reveal an explosion embedded in a ten solar mass cocoon

(Abridged) Some supernovae (SNe) may be powered by the interaction of the SN ejecta with a large amount of circumstellar matter (CSM). Here we outline a method to measure the mass of the optically thick CSM around such SNe. We present observations of SN2010jl, including the first detection of a SN using NuSTAR. The total radiated luminosity of SN2010jl is extreme, at least 9e50 erg. By modeling the visible-light data, we robustly show that the mass of the circumstellar material within ~1e16 cm of the progenitor was in excess of 10 solar masses, likely ejected tens of years prior to the SN explosion. Our modeling suggests that the shock velocity during shock breakout was ~6000 km/s, decelerating to ~2600 km/s about two years after maximum light. Our late-time NuSTAR+XMM spectra of the SN presumably provide the first direct measurement of SN shock velocity two years after the SN maximum light -- measured to be in the range of 2000 to 4500 km/s if the ions and electrons are in equilibrium, and >~2000 km/s if they are not in equilibrium. This measurement is in agreement with the shock velocity predicted by our modeling of the optical data. We also show that the mean radial density distribution of the CSM roughly follows an r^-2 law. A possible explanation for the massive CSM with a wind-like profile is that they are the result of multiple pulsational pair instability events prior to the SN explosion, separated from each other by years.