Is Integration by parts the way to go?

Calculus Level 4

01x50(lnx)150dx \int_0^1 x^{50} (\ln x)^{150} \, dx

If the value of the integral above is equal to

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

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


Bonus: Generalize 01xm(lnx)ndx \displaystyle \int_0^1 x^{m} (\ln x)^{n} \, dx .

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