Question

Integrate:
$\int \frac{1}{{\cos }^{2}x(1-\tan x{)}^2}dx$

Answer 1

$\int \frac{1}{{\cos }^{2}x{\left(1-\tan x\right)}^2}dx\Rightarrow \int \frac{{\sec }^{2}x}{{\left(1-\tan x\right)}^2}dx\Rightarrow -\int \frac{d(1-\tan x)}{(1-\tan x{)}^2}\Rightarrow \frac{1}{1-\tan x}+c$