Determine a positive integer `nlt=5` such that `int_0^1e^x(x-1)^n=16-6e`

Explanation

To solve the problem, we need to determine a positive integer \( n \) (where \( n \leq 5 \)) such that

\[ \int_0^1 e^x (x - 1)^n \, dx = 16 - 6e. \]

### Step 1: Set up the integral

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