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∫0∞⌊6ex⌋ dx=lnABC!\int _{ 0 }^{ \infty }{ \left\lfloor \frac { 6 }{ { e }^{ x } } \right\rfloor \, dx } =\ln { \frac { { A }^{ B } }{ C! } } ∫0∞⌊ex6⌋dx=lnC!AB
The above equation is true for positive integers AAA, BBB and CCC.
Find the minimum value of A+B+CA+B+CA+B+C.
Bonus: Find the generalization of ∫0∞⌊nex⌋ dx\displaystyle \int _0^\infty \left \lfloor \frac n{e^x} \right \rfloor \, dx ∫0∞⌊exn⌋dx.
Notation: !!! denotes the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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