How to compute this integration?

Question

Afternoon,

I am keeping in studying on exam and stumbled upon this integral (I am asked to count it with per-parted procedure) - $\int {2x}\arctan x\,dx$

How should I proceed the "$\arctan x$" function?

Will be grateful for every advise here :)

Answer 1

$$\int2x\arctan x\ dx=\arctan x\int2x\ dx-\int\left(\frac{d(\arctan x)}{dx}\cdot\int2x\ dx\right)dx$$

$$=\arctan x\cdot x^2-\int\frac{x^2}{1+x^2}\ dx$$

Now $\displaystyle \frac{x^2}{1+x^2}=1-\frac1{1+x^2}$