Evaluate: `inte^x\ (cotx-cos e c^2x)\ dx`

Explanation

To evaluate the integral \( I = \int e^x (\cot x - \csc^2 x) \, dx \), we will use the technique of expressing the integrand in the form of \( f(x) + f'(x) \).

### Step-by-Step Solution:

1. **Identify the Components**:
We start with the integrand \( \cot x - \csc^2 x \). We need to express this in the form \( f(x) + f'(x) \).

2. **Choose \( f(x) \)**:
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