Answer
Neither.
Work Step by Step
It is not a polynomial because the powers of $x$ are not only non-negative integers, it is not a rational function because it is not in a form of a fraction, hence it is neither.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.