Why does this integral not contradict Fubini's Theorem?

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I have the integral: $$\int^{1}_{0}\int^{\infty}_{1} (e^{-xy}-2e^{-2xy}) \,\text{d}y~\text{d}x$$, and I know that the order of integration cannot be interchanged, but why does this not contradict Fubini's Theorem? Could someone explain it in details please? Thanks.