Constant of integration 
Consider the integral  $$\int x \arctan (x) \;dx$$ Evaluate this integral using integration by parts. Then find a constant of integration that makes the last integration trivial. Compare the answers and explain any differences.

I know how to integrate by parts, I got $$\frac{x^2 \arctan (x) + \arctan (x) - x}{2} + C$$ but I don’t get the part where it asks to a find a constant of integration that makes the last trivial. 
If somebody could please explain?

$$\int x\arctan x\,dx=\left(\frac{x^2}2+C\right)\arctan x-\frac12\int\frac{x^2+2C}{x^2+1}dx.$$
Indeed, the choice $C=\dfrac12$ is advantageous.
