Let's integrate

Calculus Level 5

06exdx=lnABC!\int _{ 0 }^{ \infty }{ \left\lfloor \frac { 6 }{ { e }^{ x } } \right\rfloor \, dx } =\ln { \frac { { A }^{ B } }{ C! } }

The above equation is true for positive integers AA, BB and CC.

Find the minimum value of A+B+CA+B+C.

Bonus: Find the generalization of 0nexdx\displaystyle \int _0^\infty \left \lfloor \frac n{e^x} \right \rfloor \, dx .

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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