# Let's do some calculus! (40)

Calculus Level 5

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

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

Notations:

Inspired from Aareyan Manzoor