Is it a question or a murder weapon?

Calculus Level 5

$\Large {\prod_{r=1}^{23}} \large{ \text{exp} \left [ \displaystyle \int_0^\infty \dfrac{e^{-\left(\frac{r-24}{24} \right)t} - \left(\frac{r-24}{24} \right)e^{-t} -1 + \left(\frac{r-24}{24} \right)}{t (e^t-1)} \, dt \right ]}$

If the product above equals to $$\displaystyle \sqrt{ \dfrac{(A\pi)^B}{C} }$$ for positive integers $$A,B$$ and $$C$$, find the value of $$A+B+C$$.

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