Hint should be reworked

The current hint gives no motivation, no way for the learner to understand why it should be done this dogmatic way. The first hint should point out that there is a strategy for integrating powers of sin and cos, or draw attention to the fact that the power of cos is odd.

I agree. My recommendation in such a case is first to change the Hint tag to "bad", that is QBT (I just did so).

Do you have a suggestion on how to formulate such a hint?

I think the current hint is much better. Maybe a little on the vague side, we'll see if we get feedback from the student. I'm rating it QGH for now.