Integrating (1/(1+e^x)) dx: Challenges and Solutions

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The integral of (1/(1+e^x)) dx can be approached using substitution, specifically letting u = 1 + e^x, which simplifies the integral to a form suitable for partial fraction decomposition. Some participants suggest multiplying by e^-x to facilitate the substitution, leading to a simpler integral. There is debate over the necessity of partial fractions, with some arguing that it can be avoided depending on the substitution used. The discussion highlights common misunderstandings about logarithmic integration rules and the importance of correctly differentiating expressions. Overall, the integral can be evaluated effectively with the right substitutions and methods.
  • #31
Are you differentiating \ln(u^2 -u) wrt "x" or to "u" ?
 
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  • #32
opps I meant to type d/du
 
  • #33
camilus said:
\int{1 \over u^2-u}du = ln(u^2-u) + C
Why would you think that?



p.s. have you looked at your private messages?
 
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  • #35
Lol jesus how many mathematicians does it take to solve an exponential integral problem?

I'm not calling anyone stupid, but just found it funny ya'll are being cooperative to solve this
 
  • #36
Solve a man's integral problem, and he gets one answer. Teach a man how to solve integral problems, and he gets all of his homework done. :-p (and without cheating)
 
Last edited:
  • #37
Hurkyl said:
Solve a man's integral problem, and he gets one answer. Teach a man how to solve integral problems, and he gets all of his homework done. :-p (and without cheating)

(APPLAUSE) Well Said!
 

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