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∫01x50(lnx)150 dx \int_0^1 x^{50} (\ln x)^{150} \, dx ∫01x50(lnx)150dx
If the value of the integral above is equal to
A!BC, \dfrac{A!}{B^C}, BCA!,
where A,B,A,B,A,B, and CCC are positive integers, find the value of A+B+CA+B+CA+B+C.
Bonus: Generalize ∫01xm(lnx)n dx \displaystyle \int_0^1 x^{m} (\ln x)^{n} \, dx ∫01xm(lnx)ndx.
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