Patterns in indefinite integral (2)

This question mentioned the pattern from this indefinite integral
$$int x^n arcsin x mathrm d x$$
where “n” is a positive whole number.

What about these?
$$int x^n arctan x mathrm d x$$
$$int x^n arccos dfrac{1}{ x} mathrm d x$$
Do similar patterns occur? If so, what is the pattern? (“n” is a positive whole number)