Learn Russian: Я пробую понять правило.

The infinitive is пробовать (to try). This is a common pattern in Russian: verbs ending in -овать drop the -ова- and add -у- before the ending in the present tense. So, пробовать becomes я пробую (I try / I am trying).

Why use the perfective verb понять here instead of the imperfective понимать?

After verbs like пробовать (to try), we usually use a perfective infinitive because the focus is on achieving a specific result. You are trying to successfully grasp or "click" with the rule once (понять), rather than engaging in a continuous, open-ended background state of understanding (понимать).

Since we are learning about study verbs, how does understanding a rule differ from studying it (учить)?

This is a very important distinction! In Russian, учить правило means to study or memorize a rule through repetition (which is what учить focuses on). Понять правило, on the other hand, means to comprehend the logic of how it works. You often need to понять a rule before you can successfully учить it.

Why doesn't the ending of правило change here?

The word правило (rule) is the direct object receiving the action (the thing being understood), so it is in the accusative case. Because it is an inanimate neuter noun (ending in -о), its accusative form looks exactly the same as its dictionary (nominative) form.