1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration Y= (1/(e^x + 1))

  1. Dec 23, 2005 #1
    I seem to be having trouble with this antiderivative can i please see a solution? Y= (1/(e^x + 1))

    I tried substituting e^x + 1 as u, but that left me with the quest to find an antiderivative of 1/(u^2 - u). i feel like im missing something silly here. thanks
  2. jcsd
  3. Dec 23, 2005 #2


    User Avatar
    Homework Helper

    You have it, keep going use partial fractions: [itex] \frac{1}{u(u-1)}= -\frac{1}{u}+\frac{1}{u-1}[/itex]
  4. Dec 23, 2005 #3
    Try multiplying top and bottom by e^(-x)
  5. Jan 4, 2006 #4


    User Avatar
    Homework Helper

    Here it is (the integral)


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

    put [itex]u=e^x +1\Rightarrow x=\log (u-1) \mbox{ so that }dx=\frac{du}{u-1}[/itex]

    to get

    [tex]\int\frac{dx}{e^x +1} = \int\frac{du}{u(u-1)} = \int\left( -\frac{1}{u}+\frac{1}{u-1}\right) du = -\log |u| + \log |u-1| + C [/tex]
    [tex]= -\log \left| e^x +1\right| + \log \left| e^x\right| + C = -\log \left| e^x +1\right| + x + C[/tex]
  6. Jan 4, 2006 #5


    User Avatar
    Homework Helper

    Why on Earth are there still some people just post a complete solution (which is definitely, certainly, obviously, seriously, blah blah blah... against the forum's rules), without giving the OP an opportunity to solve the problem on his own??? :confused:
    Isn't your #2 post of this thread enough? Can't you wait for the OP to tell you if he can solve it or he still needs a little bit more help?
    Am I really missing something??? :confused:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook