esplori

One Esperanto verb covers three English ones: you esploras a coastline, a crime and a research question alike. It is transitive and takes its object bare, so no preposition creeps in the way English adds one in "research into" or "enquire about" - esplori la aferon, full stop. The root then behaves predictably: esploro is the investigation, esploristo the researcher or explorer, and esplorado the ongoing business of researching rather than any one enquiry. Where you want the narrower sense of inspecting something closely, ekzameni is the sharper choice.