(e^x)/x has no basic subsidiary - you can attempt incorporation by parts however you won't go anyplace. so mathematicians have made up an uncommon capacity called the exponential basic, Ei(x), which is characterized as: Ei(x) = essential, from - interminability to x, of (e^t/t) dt. You can't settle this unequivocally (scientifically).
Nonetheless, you can do it regarding power arrangement!
Review that
e^x = ∑ xⁿ/n!,so
e^x/x = 1/x + ∑ xⁿ/(n+1)!.
In this way,
∫e^x/x dx = ln|x| + ∑ xⁿ/(n·n!) + C.