Ei(x)=-Integral from -x to infinity of e^(-t)/t dt

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Theorem

The following formula holds: $$\mathrm{Ei}(-x) = -\displaystyle\int_{-x}^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ where $\mathrm{Ei}$ denotes the exponential integral Ei and $e^{-t}$ denotes the exponential.

Proof

References