Evaluate : `int(1)/(x^(2)"cos"^(2)((1)/(x)))dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{x^2 \cos^2\left(\frac{1}{x}\right)} \, dx \), we can follow these steps:

### Step 1: Substitution
Let's make the substitution:
\[ t = \frac{1}{x} \]
Then, we differentiate \( t \) with respect to \( x \):
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