Integrate by parts $x\cdot\arctan^2(x)$

Question

How to integrate by parts $\int x\cdot\arctan^2(x)~\mathrm{d}x$? I think this is easier to solve by substitution but I have to do this one by parts.

Thanks

P.S.: Any other helpful method or trick is obviously well accepted. Thanks.

Answer 1

HINT $\displaystyle \int x\arctan^{2}(x) = \frac{x^{2}}{2}\arctan^{2}(x) - 2\int \frac{x^2+1-1}{1+x^2}\arctan(x)$

Now integrate again.