I have to find $\int x\arctan(x)\,dx$ through inverse substitution.
Let $x = \tan\theta$, and $dx = \sec^2\theta \,d\theta$. So, we have that
$\int x\arctan(x)\,dx = \int \tan(\theta)\arctan(\tan(\theta))sec^2\theta d\theta = \int \tan(\theta)\theta \sec^2(\theta) = \int \theta \tan(\theta)(\tan^2(\theta) + 1)d\theta$.
That's about as far as I could get. I tried substituting or integrating by parts after I got to the last step, but nothing really worked.
EDIT: The problem states that we must integrate by inverse substitution.