convert/Ei converts trigonometric, hyperbolic and logarithmic integrals to exponential integrals.

$\mathrm{convert}\left(\mathrm{Si}\left(x\right)\,\mathrm{Ei}\right)$

$-\frac{\mathrm{I}\left({\mathrm{Ei}}_1\left(\mathrm{I}x\right)-{\mathrm{Ei}}_1\left(\mathrm{-I}x\right)\right)}{2}+\frac{\mathrm{csgn}\left(x\right)\mathrm{\pi }}{2}$

$\mathrm{convert}\left(\mathrm{Li}\left(x\right)\,\mathrm{Ei}\right)$

$\mathrm{Ei}\left(\ln \left(x\right)\right)$