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.

This is a part of Hot Integrals.
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