The simplify/Ei function is used to simplify expressions involving exponential integrals by applying the identities

$\mathrm{simplify}\left(\mathrm{Ei}\left(1\,\mathrm{I}x\right)+\mathrm{Ei}\left(1\,-\mathrm{I}x\right)\right)$

$-2\mathrm{Ci}\left(x\right)+\mathrm{I}\mathrm{\pi }\left(\mathrm{csgn}\left(x\right)-1\right)\mathrm{csgn}\left(\mathrm{I}x\right)$

$\mathrm{simplify}\left(\mathrm{Ei}\left(1\,\mathrm{I}x\right)-\mathrm{Ei}\left(1\,-\mathrm{I}x\right)\right)$

$\mathrm{-I}\left(\mathrm{\pi }\mathrm{csgn}\left(x\right)-2\mathrm{Si}\left(x\right)\right)$