Integrate $\int x \, \tan^{-1} (x) \, dx$ Integrate $\int x \, \tan^{-1} (x) \, dx$
My Attempt:
\begin{align}
\int x \, \tan^{-1} (x) \, dx &= \int x \, \tan^{-1} (x) \, dx \\
&= \dfrac {x^2}{2} \tan^{-1} (x) - \int \dfrac {x^2}{x^2+1} \, dx.
\end{align}

Write the integrand as $\dfrac{x^2+1-1}{x^2+1}$ and rewrite it as $1-\dfrac{1}{x^2+1}$.
