proučavati

1. to study; to research
   On već godinama proučava srpsku istoriju. — He has been studying Serbian history for years.
   Naučnici proučavaju uticaj klime na zdravlje. — Scientists are studying the effect of climate on health.
2. to study; to examine closely
   Dugo je proučavao jelovnik pre nego što je naručio. — He studied the menu for a long time before ordering.

Studying for school or an exam is učiti, not proučavati.