Is Integration by parts the way to go?

Calculus Level 4

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

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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