# Hot Integral - 9

Calculus Level 5

$\large \displaystyle \int_0^\infty \dfrac{\{ f(x) \} }{e^{xy}} \, dx = \dfrac A{y^B} \left( C - \dfrac {y^D}{e^{y^E} - F }\right)$

For $$f(x) = x - \left \lfloor x -\frac12\right\rceil$$, the equation above is true for constant positive integers $$A,B,C,D,E$$ and $$F$$. Calculate the value of $$A+B+C+D+E+F$$.

Clarifications:

• $$\lfloor \cdot \rceil$$ represents the nint function (nearest integer function).

• $$\{ \cdot \}$$ represents the fractional part function.

×