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$\int_0^1 x^{50} (\ln x)^{150} \, dx$

If the value of the integral above is equal to

$\dfrac{A!}{B^C},$

where $A,B,$ and $C$ are positive integers, find the value of $A+B+C$.

Bonus: Generalize $\displaystyle \int_0^1 x^{m} (\ln x)^{n} \, dx$.

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