Is there a general formula for $\int{\big(\frac {\arctan x}{x^2+1} \big )}^{\frac1k}dx$ , with $k$ is positive integer?

Question

I'm interested to know if there is a general formual for $$ \int\left[\arctan\left(x\right) \over x^{2} + 1\right]^{1/k}\mathrm{d}x $$ with $k$ is positive integer may present integral of fraction derivative in other context for the form : $u'\times u$ , For the power is integer there is for each $k$ an antiderivative , But for fraction power i didn't find that in web , then is there any reference or any paper where the closed form of the titled integral is defined and exists ?.