Integration involving complex exponentials

[Jadaav]

Homework Statement

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

Homework Equations

No substitutions have been given.

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.

 

[pasmith]

Homework Statement

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

Homework Equations

No substitutions have been given.

The Attempt at a Solution

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

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

I haven't been able to do it. I don't really know where to start.

Consider the substitution u = e^x.

 

[Jadaav]

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 ?

 

[slider142]

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 ?

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.

 

[Jadaav]

OK thanks.

I'll start working on it.