Question

Integrate e^(2x)*((2x-1)/(4(x)^2))^2

My thoughts on this question :

I simplfied the terms after the "*" to get three separate integrals :
integrate (e^(2x)) + ((e^(2x))/4(x^2)) + ((e^(2x))/x)

The answer for the first integral is obvious and then I was able to simplify 2nd to the form of 3rd and I don't see a way to integrate the 3rd one. I need help on solving the 3rd integral.
Thanks!

Answer 1

The 3rd one cannot be done using elementary functions.
It involves Ei(x), the exponential integral, which is just defined as
∫ e^x / x dx

Answer 2

Thanks @oobleck.
Is there any other way to solve this using elementary functions without involving the integral e^(x)/x?

Answer 3

Well, I guess you could reduce it to an infinite series and integrate term by term.
Not very satisfying though ...