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Simplify the Laplace Transform for $E_{i}(-y)^{2}$

I want to simplify the Laplace transform expression of $E_{i}(-y)^{2}$, where $E_{i}(y)$ is the exponential integral defined by $E_{i}(y) = -\int\limits_{-y}^{\infty} \frac{e^{-t}}{t} dt$. Question: ...
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