How to integrate tan^-1(x)

Published On :2021-01-27 16:44:00

[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}]