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Integration involving complex exponentials

  1. Sep 15, 2014 #1
    1. The problem statement, all variables and given/known data

    [itex]\int[/itex][itex][[/itex]( e^x + 4 )/ (4e^x + 1) [itex]][/itex]^2

    2. Relevant equations

    No substitutions have been given.

    3. The attempt at a solution

    I've tried using the method of f' (x)/f (x). But it was in vain.

    I haven't been able to do it. I don't really know where to start.
     
    Last edited: Sep 15, 2014
  2. jcsd
  3. Sep 15, 2014 #2

    pasmith

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    Homework Helper

    .. because clearly the numerator is not the derivative of the denominator.

    Consider the substitution [itex]u = e^x[/itex].
     
  4. Sep 15, 2014 #3
    Actually I was thinking about the substitution. But I have one question; an exponential function is not linear. So if I use substitution does it become a linear one ?
     
  5. Sep 15, 2014 #4
    No. Your function will become a rational function. You will then be able to integrate it by following the method of partial fractions to separate it into a sum of known integrals.
     
  6. Sep 15, 2014 #5
    OK thanks.

    I'll start working on it.
     
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