udu substitution

[intervade]

Ok, here is my problem

the indefinite integral of (e^x)/(e^(2x)+2e^x+1))

Now, I'm sort of lost, maybe I'm on the right track, I don't know. I let u = e^(2x)+2e^x+1 .. so du = 2(e^2x+e^x)dx .. but I'm not sure that gets me anywhere or I can't see where to go next.

Help would be much appreciated!

 

[daon]

Let \(\displaystyle u=e^x\).

Then solve

\(\displaystyle \int \frac{du}{(u+1)^2}\)

 

[BigGlenntheHeavy]

\(\displaystyle \int\frac{e^{x}}{e^{2x}+2e^{x}+1}dx \ = \ \int\frac{e^{x}}{(e^{x}+1)^{2}}dx\)

\(\displaystyle Can \ you \ take \ it \ from \ here?\)

 

[chrisr]

You may also let

\(\displaystyle u=e^x+1\)

 

[daon]

You may also let

\(\displaystyle u=e^x+1\)

Yes, this is most efficient.