\[\large \displaystyle \int_2^{100} (H_x + H_{x-1} + H_{x-2}) \, dx = \log ( A \times (B!)^3 ) + C \gamma \]

The above equation holds true for positive integers \(A, B, C \) where \(B\) is the largest possible integer. Find \( A + B + C \).

**Notations:**

- \(H_n\) denotes the generalized harmonic number.
- \(\gamma\) denotes the Euler-Mascheroni constant.
- \(\log (\cdot)\) denotes the natural logarithm function, that is \(\log_{e}{(\cdot)}\) or \(\ln(\cdot)\).
- \(k!\) denotes the factorial notation, that is \(k! = k(k-1)(k-2)...\ 3\cdot2\cdot1\)

Inspired from Aareyan Manzoor

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