Question

Solve $\int \frac{x}{{\cos }^{2}x}dx$

Answer 1

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

$=x\int se{c}^{2}xdx-\int \frac{d}{dx}\left(x\right)\int {\sec }^{2}xdx$

$=x\tan x-\int \tan x+c$

$=x\tan x+\log |\cos x|+c$