Evaluate: `int1/(2-3cos2x)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{2 - 3 \cos 2x} \, dx \), we will follow these steps:

### Step 1: Use the half-angle identity for cosine
We know that \( \cos 2x = \frac{1 - \tan^2 x}{1 + \tan^2 x} \). Thus, we can rewrite the integral as:
\[ I = \int \frac{1}{2 - 3 \left( \frac{1 - \tan^2 x}{1 + \tan^2 x} \right)} \, dx \]

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