Question

Evaluate: $\int \frac{\tan x}{{\left(\cos x\right)}^2}dx$

Answer 1

$\begin{array}{c}Letu=\tan x\\ du={\sec }^{2}xdx\\ Now,\\ \int \frac{\tan x}{{\left(\cos x\right)}^2}dx\\ =\int \tan xse{x}^{2}xdu\\ =\int udu\\ =\frac{u^2}{2}\\ =\frac{1}{2}{\tan }^{2}x+C\end{array}$