Prove that if $\bigtriangledown \times F=0,$ then $\exists u$ such that $F= \bigtriangledown u$

Question

If $\bigtriangledown \times F=0,$ then $\exists $ a function $u$ such that $F= \bigtriangledown u$

The converse is straightforward to prove, but this statement is giving a hard time.

Any hints/tips/tricks?

Thank youuu!