Je vais à la bibliothèque pour étudier.
English: I go to the library to study.
The 'expression du but' in French is how you express the purpose, goal, or intention of an action. It answers the question 'why?' or 'for what purpose?'.
Use these forms in French when you want to explain the reason or goal behind an action, such as why you do something or what you hope to achieve.
Je vais à la bibliothèque pour étudier.
English: I go to the library to study.
Elle travaille afin de gagner de l’argent.
English: She works in order to earn money.
Nous faisons du sport dans le but de rester en forme.
English: We do sports in order to stay fit.
Il parle lentement pour que tout le monde comprenne.
English: He speaks slowly so that everyone understands.