How to solve ∫x/(1+e^x) dx

[all-black]

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 + e^x) dx


please help me to solve this.. :)

 

[micromass]

You can't solve this. This integral cannot be solved in terms of elementary functions. Specifically, you need the polylogarithm to solve this.

 

[all-black]

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? :)

 

[Number Nine]

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?

 

[all-black]

Do you have any background in complex analysis?

yess.. but not so deep.. just a basic of complex analysis..

 

[vishalhd]

this problem cannot be solved normally. you can use integration by parts

integration by parts is this: ∫ u dv = u.v - ∫ v du

 

[HallsofIvy]

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.

 

[JJacquelin]

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 :