MHB Evaluating Integral of $x(tan^{-1}(x))^2$

[wonguyen1995]

Find \int_{}^{} x*(tan^(-1)(x))^2\,d

 

[MarkFL]

What are the limits of integration, if any?

What have you tried so far?

 

[Prove It]

Find \int_{}^{} x*(tan^(-1)(x))^2\,d

I would attempt integration by parts with $\displaystyle \begin{align*} u = \left[ \arctan{(x)} \right] ^2 \end{align*}$ and $\displaystyle \begin{align*} \mathrm{d}v = x\,\mathrm{d}x \end{align*}$...

 

[wonguyen1995]

I would attempt integration by parts with $\displaystyle \begin{align*} u = \left[ \arctan{(x)} \right] ^2 \end{align*}$ and $\displaystyle \begin{align*} \mathrm{d}v = x\,\mathrm{d}x \end{align*}$...

I did it but it needs many steps and there is no result

 

[Prove It]

I did it but it needs many steps and there is no result

Then show us what you tried and where you got stuck...