udu substitution

intervade

New member
Joined
Apr 6, 2009
Messages
49
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!
 
Let u=ex\displaystyle u=e^x.

Then solve

du(u+1)2\displaystyle \int \frac{du}{(u+1)^2}
 
exe2x+2ex+1dx = ex(ex+1)2dx\displaystyle \int\frac{e^{x}}{e^{2x}+2e^{x}+1}dx \ = \ \int\frac{e^{x}}{(e^{x}+1)^{2}}dx

Can you take it from here?\displaystyle Can \ you \ take \ it \ from \ here?
 
Top