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

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 ?.

• I seriously doubt a closed form exists. Do you have any reason to think it does? Also: what have you tried? – clathratus Apr 1 at 1:20
• $x=\tan u$ gives $$\int\left[\frac{u}{\sec(u)^2}\right]^{1/k}\sec(u)^2du$$ which is $$\int u^{1/k}\cos(u)^{2/k-2}du$$ I am sure there is no closed form – clathratus Apr 1 at 1:24