How Do You Integrate e^-x / (1 + e^-x) dx?

[menco]

Homework Statement

(e^-x)/(1+e^-x)dx

Homework Equations

Integral of e^x function

The Attempt at a Solution

I am completely lost with the problem, the fact that it is e^-x and not e^x has me stupped as well as the division.

 

[foxjwill]

Try $u$-substitution.

 

[menco]

so if I let u=1+e^-x?

 

[Dickfore]

yes?

 

[foxjwill]

so if I let u=1+e^-x?

Well, does it work?

 

[menco]

I still can't figure it out so I gave up and will try again later

 

[foxjwill]

I still can't figure it out so I gave up and will try again later

When you do get back to it, answer this: What is $du$ when $u=1+e^{-x}$?

 

[menco]

Will du = -e^-x dx