Currently, the only library which works for the quest is the royal library, so you must become a noble and then ask the emperor about gaining access to it. He gives you access if you meet some requirements (either if you are part of his harem, if you completed a specific quest for him before, or if your relationship with him is 5 or more).
I plan to add at least 1 more library in the future where such a research is possible, but for now that's the only one.