Hello everyone,

I have been having a lot of trouble from a seemingly simple integral:

$\displaystyle

\int arctan (arctan x)dx

$.

I say that it's trivial because $\displaystyle arctan (arctan x)$ is a function that can be plotted and does not go to infinity anywhere. In fact, it looks more or less like arctan, which does have an integral.

Trying to plug it into mathematica yields no results, so I was wondering if there was an integral, and if so, how it should be approached.

I tried integration by parts, substitution, and integration by parts again, but all I ended up with was $\displaystyle \int sec^2 (u) * arctan (u) du$, where $\displaystyle x=tan u$.

Assistance would be very greatly appreciated!

P.S. Attached is work done and graphs of some important functions as mentioned above, but really getting nowhere...