Question

Evaluate

$I=\int {\tan }^{-1}\left(x\right)dx$

Answer 1

$\begin{array}{c}{I}_3=\int {\tan }^{-1}\left(x\right)dx\\ =x{\tan }^{-1}x-\frac{1}{2}\log \left(1+x^2\right)+C\end{array}$