Question

$\text{Evalute}\int \frac{{\sec }^{2}x}{3+\tan x}dx.$

Answer 1

$I=\int \frac{se{c}^{2}x}{3+tanx}dx$

Let $tanx=t$

$se{c}^{2}xdx=dt$

$I=\int \frac{dt}{3+t}$

$=log|3+t|+c$

$=log|3+tanx|+c$