Question Number 89213 by cindiaulia last updated on 16/Apr/20
$$\int\frac{\sqrt{\mathrm{tan}\:\mathrm{x}\:+\:\mathrm{1}}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} \\ $$
Answered by $@ty@m123 last updated on 16/Apr/20
$$\int\sqrt{\mathrm{tan}\:\mathrm{x}\:+\:\mathrm{1}}\:.\mathrm{sec}\:^{\mathrm{2}} {xdx} \\ $$$$\int\sqrt{\mathrm{1}+{t}}{dt}\:,\:\:{t}=\mathrm{tan}\:{x} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{1}+{t}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\mathrm{C} \\ $$