Need a little help starting this integral

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    Integral
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Homework Help Overview

The discussion revolves around the integral of the function \(\frac{1}{e^x+1}\). Participants are exploring various methods of integration, including substitution and integration by parts, while seeking guidance on their approaches.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts substitution, partial fraction decomposition, and integration by parts but struggles to find a solution. A participant suggests multiplying by \(e^{-x}\) as a hint. Others discuss the validity of their integration steps and express uncertainty about their results.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the correctness of their methods. Some express a desire for confirmation of their reasoning, indicating a collaborative effort to build understanding rather than reaching a definitive conclusion.

Contextual Notes

Participants are navigating the complexities of integration techniques and expressing concerns about their confidence in the process. There is a focus on understanding the steps involved rather than simply arriving at an answer.

silverdiesel
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[tex]\int\frac{1}{e^x+1}dx[/tex]

I have tried substitution, partial fraction decomposition, and integration by parts but I can't seem to figure it out. Any help is much appriciated. o:)
 
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Hint: multiply top and bottom by [tex]e^{-x}[/tex].
 
okay, then I can use u sub, which nets...

[tex]-ln (1+e^{-x})[/tex]

is that right?
 
Last edited:
That does not seem right. What I have I done wrong?

[tex]\int\frac{e^{-x}}{1+e^{-x}}dx[/tex]

[tex]u = 1+e^{-x}\\-du = e^{-x}[/tex]

[tex]-\int\frac{1}{u}du[/tex]
 
Last edited:
silverdiesel said:
That does not seem right. What I have I done wrong?

[tex]\int\frac{e^{-x}}{1+e^{-x}}dx[/tex]

[tex]u = 1+e^{-x}\\-du = e^{-x}[/tex]

[tex]-\int\frac{1}{u}du[/tex]

It looks right to me, why do you think it's wrong?
 
After further review, I don't think its wrong. I guess I am just working on building confidence in the integration process and I was hoping for some confirmation that is was done right. Thank you. These forums have been extremely helpful and I really appreciate all the quick and intelligent responces.
 

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