Efficiently Solve ∫x/(1+ex) dx with Expert Guidance | Get Back on Track Now!

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In summary, the conversation discusses the integral of x divided by 1+ex and the inability to solve it in terms of elementary functions. It is suggested to use the polylogarithm function to solve it, but the person asking for help only has a basic understanding of complex analysis. Integration by parts is mentioned as a possible method, but it is also noted that this integral cannot be solved normally and will require the use of polylogarithm.
  • #1
all-black
13
0
i just found this and try to solve.. but then since i left all of these for many years, so i can't remember some of the ways..

i will keep thinking of this because I'm not able to solve it.. and this make me suffer..

∫ x / (1 + ex) dx


please help me to solve this.. :)
 
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  • #2
You can't solve this. This integral cannot be solved in terms of elementary functions. Specifically, you need the polylogarithm to solve this.
 
  • #3
micromass said:
You can't solve this. This integral cannot be solved in terms of elementary functions. Specifically, you need the polylogarithm to solve this.

ohh... i see... thank you micromass...
but if you want to.. can you show how to solve this by using the polylogarithm? :)
 
  • #4
all-black said:
ohh... i see... thank you micromass...
but if you want to.. can you show how to solve this by using the polylogarithm? :)

Do you have any background in complex analysis?
 
  • #5
Number Nine said:
Do you have any background in complex analysis?

yess.. but not so deep.. just a basic of complex analysis..
 
  • #6
this problem cannot be solved normally. you can use integration by parts

integration by parts is this: ∫ u dv = u.v - ∫ v du
 
  • #7
What do you mean by that? "Integration by parts" is a normal integration method. And won't work here. As micromass said, that cannot be integrated in terms of elementary functions.
 
  • #8
all-black said:
ohh... i see... thank you micromass...
but if you want to.. can you show how to solve this by using the polylogarithm? :)

If you know the polylogarithm functions, then the formal result is :
 

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FAQ: Efficiently Solve ∫x/(1+ex) dx with Expert Guidance | Get Back on Track Now!

How do I approach solving this problem?

To solve a problem, it's important to first understand what the problem is asking and what information is provided. Then, break the problem down into smaller, more manageable parts and use logical reasoning and critical thinking skills to find a solution.

What should I do if I get stuck while solving this problem?

If you get stuck while solving a problem, take a step back and try to approach the problem from a different angle. You can also try breaking the problem down into smaller parts or seeking help from a peer or teacher.

How can I improve my problem-solving skills?

To improve your problem-solving skills, practice regularly and challenge yourself with new and difficult problems. It's also helpful to approach problems with a positive and open-minded attitude and to seek feedback from others.

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