Inspiration is in the air

Calculus Level 5

\[\large \displaystyle \int_{0}^\infty\lfloor x+1\rfloor\dfrac{(-1)^{\lfloor x\rfloor}\cdot 2016\cdot { \{x\} }\cdot dx}{2^{\lceil x\rceil}} = \, ? \]

Notations:


Inspiration.

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