`int1/(cos^2x(1-tanx)^2)\ dx`

Explanation

To solve the integral \(\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx\), we will follow these steps:

### Step 1: Rewrite the Integral
First, we can rewrite \(\cos^2 x\) in terms of secant:
\[ \int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx = \int \frac{\sec^2 x}{(1 - \tan x)^2} \, dx \]

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