Identify the (Infinitive, Gerund, Participle, Dangling Participle, or Absolute) Phrase in the following sentence

I went to the library to study for my Spanish exam.

An infinitive is a verbal (not a verb) that functions as a noun, adjective, or adverb. It usually consists of the word " to " followed by the verbal.

I went to the library (to study) for my Spanish exam.

" to study " is an infinitive and it is functioning as an adverb modifying the verb " went"