Exponential Integral Problem help

**FPCPineapple** · August 19th 2009, 11:27 PM

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!

**red_dog** · August 19th 2009, 11:33 PM

$\int\frac{e^{2x}}{e^x+1}dx=\int\frac{e^x}{e^x+1}\c dot e^xdx$

The substitution is $e^x=u$

**simplependulum** · August 19th 2009, 11:36 PM

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

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

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

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

**FPCPineapple** · August 20th 2009, 07:13 AM

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!!!

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