Question

Integrate $\int \frac{{\sec }^{2}x}{\tan x}dx$

Answer 1

$\int \frac{{\sec }^{2}x}{tanx}dx$

Let $tanx=t$

$\frac{dt}{dx}={\sec }^{2}x$

$dt={\sec }^{2}xdx$

$\int \frac{dt}{t}=lnt+C$

$=ln\left|tanx\right|+C$