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

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Homework Help Overview

The problem involves integrating the function (e^-x)/(1 + e^-x) with respect to x. The subject area pertains to calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the possibility of using u-substitution, with one suggesting u = 1 + e^-x. Questions arise regarding the effectiveness of this substitution and the resulting differential du.

Discussion Status

The discussion is ongoing, with some participants expressing confusion about the integration process and the substitution method. Guidance has been offered regarding the substitution, but there is no clear consensus on the next steps or resolution.

Contextual Notes

One participant notes difficulty due to the presence of e^-x and the division in the integrand. There is an indication of frustration with the problem, and some participants have expressed a need to revisit the topic later.

menco
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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.
 
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Try u-substitution.
 
so if I let u=1+e^-x?
 
yes?
 
menco said:
so if I let u=1+e^-x?

Well, does it work?
 
I still can't figure it out so I gave up and will try again later
 
menco said:
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}?
 
Will du = -e^-x dx
 

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