Evaluate: `int(8cotx+1)/(3cotx+2)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{8 \cot x + 1}{3 \cot x + 2} \, dx \), we will follow these steps:

### Step 1: Rewrite the integral
We start by rewriting the integral in a more manageable form. We can express the cotangent function in terms of sine and cosine:
\[ \cot x = \frac{\cos x}{\sin x} \]
Thus, we can rewrite the integral as:
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