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: Integral with e^x in it

  1. Sep 6, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{1+e^{x}}{1-e^{x}}[/tex] dx

    2. Relevant equations

    3. The attempt at a solution
    I've tried substituting for u=e^x or u=1-e^x but I can't seem to get anywhere. Haven't done calc in a while and just want someone to point me in the right direction. Thanks.
    Last edited: Sep 6, 2009
  2. jcsd
  3. Sep 6, 2009 #2
    Letting [itex] u = e^x [/tex] gives
    Next expand in partial fractions. The integrand becomes
    \frac{2}{1-u} + \frac{1}{u}
    which you can easily integrate.
    Last edited: Sep 7, 2009
  4. Sep 6, 2009 #3
    I'm thinking [tex]u=e^{x}[/tex] might work, at least for x<0.

    Also, [tex]{{1+u}\over{1-u}}={{1-u+2u}\over{1-u}}=1+2{{u}\over{1-u}}[/tex]
    Last edited: Sep 6, 2009
  5. Sep 6, 2009 #4
    For x>0, you might try [tex]u=e^{-x}[/tex]


    Last edited: Sep 6, 2009
  6. Sep 7, 2009 #5


    User Avatar
    Homework Helper

    Well, why can't you sub u = ex, when x > 0?
  7. Sep 7, 2009 #6


    User Avatar
    Science Advisor

    You can- it really doesn't make any difference.
  8. Sep 7, 2009 #7
    Thanks a lot guys.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook