Question Number 197744 by mathlove last updated on 27/Sep/23
$$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$
Answered by witcher3 last updated on 27/Sep/23
$$\int\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{dx}=\mathrm{2xtan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\int\frac{\mathrm{2x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$$$=\mathrm{xtan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)+\mathrm{c},\mathrm{c}\in\mathbb{R} \\ $$