Asked by Arya_S
                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!
            
        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!
Answers
                    Answered by
            oobleck
            
    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
    
It involves Ei(x), the exponential integral, which is just defined as
∫ e^x / x dx
                    Answered by
            Arya_S
            
    Thanks @oobleck.
Is there any other way to solve this using elementary functions without involving the integral e^(x)/x?
    
Is there any other way to solve this using elementary functions without involving the integral e^(x)/x?
                    Answered by
            Anonymous Bosh!
            
    Well, I guess you could reduce it to an infinite series and integrate term by term.
Not very satisfying though ...
    
Not very satisfying though ...
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