# Integration involving complex exponentials

1. Sep 15, 2014

1. The problem statement, all variables and given/known data

$\int$$[$( e^x + 4 )/ (4e^x + 1) $]$^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. Sep 15, 2014

### pasmith

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

Consider the substitution $u = e^x$.

3. Sep 15, 2014

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 ?

4. Sep 15, 2014

### slider142

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.

5. Sep 15, 2014