Exponential Integral Problem help

• Aug 19th 2009, 11:27 PM
FPCPineapple
Exponential Integral Problem help
Hi everyone, I'm currently really really stumped on this question...I've even tried working backwards but can't seem to get it...well heres the question, hopefully someone can help me out!

find the integral of:

e^(2x)*dx/(e^x +1)

I'm assuming we use substitution or integration by parts? does the equation need to be manipulated first?

Thanks! :)
• Aug 19th 2009, 11:33 PM
red_dog
$\int\frac{e^{2x}}{e^x+1}dx=\int\frac{e^x}{e^x+1}\c dot e^xdx$

The substitution is $e^x=u$
• Aug 19th 2009, 11:36 PM
simplependulum
$\int \frac{e^{2x} dx}{e^x+1}$

$= \int \frac{ e^{2x} + e^x - e^x }{e^x+1}~dx$

$= \int (e^x - \frac{e^x}{e^x+1} )~dx$

$= e^x - \int \frac{d(e^x)}{e^x+1}$
• Aug 20th 2009, 07:13 AM
FPCPineapple
Quote:

Originally Posted by simplependulum
$\int \frac{e^{2x} dx}{e^x+1}$

$= \int \frac{ e^{2x} + e^x - e^x }{e^x+1}~dx$

$= \int (e^x - \frac{e^x}{e^x+1} )~dx$

$= e^x - \int \frac{d(e^x)}{e^x+1}$

Thank you very much, I finally understand it! I had a feeling I was suppose to manipulate the question somehow, thanks!!!