Formal:
* Examine: To inspect or study something closely and carefully.
* Scrutinize: To examine something very carefully in order to find errors or problems.
* Dissect: To break something down into its parts and study them separately.
* Investigate: To try to find out the facts about something.
* Evaluate: To form an opinion about the worth or quality of something.
* Assess: To make a judgment about the value, importance, or quality of something.
* Interpret: To explain the meaning of something.
Informal:
* Break down: To separate something into its parts to understand it better.
* Figure out: To understand something by thinking about it carefully.
* Pick apart: To examine something closely and critically.
* Study: To learn about something by reading, observing, or thinking about it.
* Probe: To explore something in detail.
Other options:
* Deconstruct: To break something down into its fundamental parts.
* Deduce: To reach a conclusion by reasoning.
* Synthesize: To combine different ideas or pieces of information to create something new.
The best word to use will depend on the context and the specific type of analysis being performed.