# Let's integrate

Calculus Level 5

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

The above equation is true for positive integers $$A$$, $$B$$ and $$C$$, find $$A+B+C$$.

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



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

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

×