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

The following formula holds for $x>0$: $$\mathrm{Ei}(x) = \mathrm{PV} -\displaystyle\int_{-x}^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ where $\mathrm{Ei}$ denotes the exponential integral Ei, $\mathrm{PV}$ denotes the Cauchy principal value, and $e^{-t}$ denotes the exponential.