Question

How to integrate this function here

Answer 1

\(\int \frac{e^{-x}}{x}dx\)

Answer 2

(e^-x)/x has no elementary derivative -- you can try integration by parts but you won't get anywhere.

so mathematicians have made up a special function called the exponential integral, Ei(x), which is defined as:

Ei(x) = integral, from -infinity to x, of (e^t / t) dt.

Answer 3

So I integrate like improper integral?