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: 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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook