Question

Solve:
$\int \frac{{\sec }^{2}x}{\cos e{c}^{2}x}dx$

Answer 1

Consider the given function

$\int \frac{{\sec }^{2}x}{\cos e{c}^{2}x}dx$

$=\int \frac{1}{\frac{{\cos }^{2}x}{\frac{1}{{\sin }^{2}x}}}dx$

$=\int \frac{{\sin }^{2}x}{{\cos }^{2}x}dx$

$=\int {\tan }^{2}xdx$

$=\int ({\sec }^{2}x-1)dx$

$=\int {\sec }^{2}xdx-\int 1dx$

$=\tan x-x+C$

Hence, this is the aanswer.