Question Number 176187 by gloriousman last updated on 14/Sep/22
$$\int\frac{\mathrm{dy}}{\mathrm{tan}^{−\mathrm{1}} \mathrm{y}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)} \\ $$
Answered by BaliramKumar last updated on 14/Sep/22
$$\int\frac{\mathrm{dy}}{\mathrm{tan}^{−\mathrm{1}} \mathrm{y}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)} \\ $$$$ \\ $$$${put}\:\:\:\:\:\:\:\:\:{tan}^{−\mathrm{1}} \left({y}\right)\:=\:{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{\mathrm{1}+{y}^{\mathrm{2}} }\:=\:{dx} \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx}\:=\:{ln}\mid{x}\mid\:+\:\mathrm{C} \\ $$$$\int\frac{\mathrm{dy}}{\mathrm{tan}^{−\mathrm{1}} \mathrm{y}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)}\:=\:{ln}\mid{tan}^{−\mathrm{1}} \left({y}\right)\mid\:+\:\mathrm{C} \\ $$$$ \\ $$