If I'm solving a version of the following integral
$\int \log(x)e^x dx$
how does the exponential integral arise as a solution to this? (Or is it much too theoretical to explain simply?) I do a much more complicated version of this on WolframAlpha.com and the Ei(x) function is used, but it is used with the above integral too, and no steps are given.
I understand the form of Ei(x), but thought that someone might be able to explain how it arises as a solution to the above.