\[ \large \int_0^\infty e^{-x} (\ln x)^2 \, dx = A \gamma ^B + \zeta(C) \]

The equation above holds true for integer constants \(A,B\) and \(C\). Find \(A+B+C\).

**Notations**:

\( \gamma\) denote the Euler-Mascheroni constant.

\(\zeta(\cdot) \) denotes the Riemann zeta function.

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