\[\begin{array}{l} \int \tan ^{-1} x \mathrm{~d} x \\\\ \text { By Parts } \\\\ \text { Let } \Rightarrow u=\tan ^{-1} x \quad d v=1 \\\\ \qquad d u=\frac{1}{1+x^{2}} \quad v=x \\\\ x \tan ^{-1} x-\int \frac{x}{1+x^{2}} d x \\\\ x \tan ^{-1} x-\frac{1}{2} \ln \left|1+x^{2}\right|+c\\ \end{array}\]
Tags:
integration