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Integrate the following:
∫0∞ ⌊2e−x⌋dx,\int_0^\infty \! \left\lfloor 2e^{-x} \right\rfloor dx, ∫0∞⌊2e−x⌋dx,
where ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ denotes the greatest integer function.
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