How to integrate tan^-1(x)

 

$$\begin{array}{l}\int {\tan }^{-1}x\mathrm{d}x\\ \\ \text{ By Parts }\\ \\ \text{ Let }\Rightarrow u={\tan }^{-1}xdv=1\\ \\ du=\frac{1}{1+x^2}v=x\\ \\ x{\tan }^{-1}x-\int \frac{x}{1+x^2}dx\\ \\ x{\tan }^{-1}x-\frac{1}{2}\ln |1+x^2|+c\end{array}$$