Results 1 to 2 of 2

Thread: e^x integral

  1. #1
    Senior Member polymerase's Avatar
    Joined
    May 2007
    From
    Sydney
    Posts
    267

    e^x integral

    Find $\displaystyle \int \frac{1+e^x}{1-e^x}$

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,656
    Thanks
    14
    Quote Originally Posted by polymerase View Post
    Find $\displaystyle \int \frac{1+e^x}{1-e^x}$
    $\displaystyle \int {\frac{{1 + e^x }}
    {{1 - e^x }}\,dx} = \int {\frac{{1 - e^x + 2e^x }}
    {{1 - e^x }}\,dx} = \int {dx} - 2\int {\frac{{\left( {1 - e^x } \right)'}}
    {{1 - e^x }}\,dx}.$

    So $\displaystyle \int {\frac{{1 + e^x }}
    {{1 - e^x }}\,dx}=x - 2\ln \left| {1 - e^x } \right| + k.$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Aug 31st 2010, 07:38 AM
  2. Replies: 1
    Last Post: Jun 2nd 2010, 02:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 01:52 PM
  4. Replies: 0
    Last Post: Sep 10th 2008, 07:53 PM
  5. Replies: 6
    Last Post: May 18th 2008, 06:37 AM

Search Tags


/mathhelpforum @mathhelpforum