Question Number 12102 by Nayon last updated on 13/Apr/17
$${Evaluate}\:\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}{dx} \\ $$
Answered by sma3l2996 last updated on 13/Apr/17
$${A}=\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}} {x}}{dx}={tan}\left({x}\right)+{C} \\ $$
Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 13/Apr/17
$${I}=\int\frac{{dx}}{{cos}^{\mathrm{2}} {x}}=\int\left(\mathrm{1}+{tg}^{\mathrm{2}} {x}\right){dx} \\ $$$$=\int{dx}+\int{tg}^{\mathrm{2}} {xdx}={x}+{tgx}−{x}+{C}={tgx}+{C} \\ $$