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!

Misc integral

  1. Mar 29, 2010 #1
    [tex]
    \int \frac{1+e^x}{1-e^x}dx
    [/tex]
    [tex]
    \int \frac{dx}{1-e^x} +\int \frac{e^x}{1-e^x}dx
    [/tex]
    [tex]
    u=e^x
    [/tex]
    [tex]
    lnu=x
    [/tex]
    [tex]
    \frac{du}{u}=dx
    [/tex]
    [tex]
    \int \frac{du}{u(1-u)}+\int \frac{du}{1-u}
    [/tex]
    [tex]
    \int \frac{A}{u}+\frac{B}{1-u}du -ln|1-u|+C
    [/tex]
    [tex]
    ln|e^x|+ln|1-e^x|-ln|1-e^x|+C
    [/tex]
    [tex]
    x+C
    [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 29, 2010 #2

    Mark44

    Staff: Mentor

    Your antiderivative is obviously incorrect, since d/dx(x + C) = 1. Your antiderivative would have been correct if its derivative was (1 + e^x)/(1 - e^x).

    It might be easier not to split into two integrals, but using the same substitution. If you do that, you'll get something you can use partial decomposition on.
     
  4. Mar 30, 2010 #3
    [tex]
    x-2ln|1-e^x|+C
    [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Misc integral
  1. Misc. Questions (Replies: 2)

  2. Misc integral (Replies: 2)

  3. Misc integral (Replies: 2)

  4. Misc integral (Replies: 2)

  5. Misc integral (Replies: 3)

Loading...