Find the smallest integral value of x satisfying `(x-2)^(x^(2)-6x+8) gt 1`.

Explanation

To solve the inequality \((x-2)^{(x^2 - 6x + 8)} > 1\), we will analyze the expression by considering different cases for the base \(x-2\).

### Step 1: Identify Cases Based on the Base
We will consider the following cases:
1. Case 1: \(x - 2 > 1\)
2. Case 2: \(x - 2 < 1\)
3. Case 3: \(x - 2 = 1\) (This case can be ignored since we need \(>\) not \(\geq\))

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