Question

How to solve (integ.)[ e^x / x ] dx ?

Answer 1

initial question: (integ.)[ e^x / x^2 ] dx ?

Answer 2

for initial question, use integration by parts

u = e^x ............... dv = x^-2
du = e^x .............. v = -1/x dx

--> -e^x/x + integral [e^x/x dx]

do integration by parts again
u = e^x ............... dv = 1/x
du = e^x .............. v = ln(x) dx

--> -e^x/x +ln(x)e^x - integral [ln(x)e^x dx]

do integration by parts again
u = ln(x)e^x .................. dv = dx
du = e^x/x +ln(x)e^x .............. v = x dx

this keeps going it looks like so the integral can't be solved using regular methods
see wolfram
http://www.wolframalpha.com/input/?i=integrate+e^x%2Fx+dx