Question

Evaluate $\int \frac{{\sec }^{2}x}{3+\tan x}dx$

Answer 1

$I=\int \frac{{\sec }^{2}x}{3+\tan x}dx$
Let $3+\tan x=t⟹{\sec }^{2}xdx=dt$
$\therefore I=\int \frac{1}{t}dt$
$⟹I=\ln |t|+C$
$⟹I=\ln (|3+\tan x|)+C$