Results 1 to 8 of 8

Math Help - Integral of x/[1+exp(x)] dx

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    5

    Integral of x/[1+exp(x)] dx

    \int_0^{10}(\frac{300x}{1+e^x})dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by ragungs View Post
    \int_0^{10}(\frac{300x}{1+e^x})dx
    There is no closed form expression for this integral. Are you looking for an approximation?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    5
    I need the true value of this integral to calculate the error of my approximation.

    I wonder if this integral can be solved by hand.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by ragungs View Post
    I need the true value of this integral to calculate the error of my approximation.

    I wonder if this integral can be solved by hand.
    As I said there is no closed form expression. You cannot get an exact value of it.
    \int \frac{x}{1 + e^x}~dx = \frac{x^2}{2} - ln(1 + e^x) - \sum_{n = 1}^{\infty} \frac{e^{nx}}{n^2}

    There is no expression for that summation in terms of elementary functions. This thing can only be approximated.

    -Dan

    Edit: A made a mistake in copying "polylog" function from the Integrator site. I have fixed it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    652
    Thanks
    2
    Awards
    1
    \int_0^{10} \left(\frac{300x}{1 + e^x}\right)dx \approx 246.59029

    I used my graphing calculator to calculate the integral... It's not exact either, but it's closer than a lot of people can get.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2008
    Posts
    5
    ok thanks all.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by topsquark View Post
    There is no closed form expression for this integral. Are you looking for an approximation?

    -Dan
    It does in terms of the polylogarithm {\rm Li}_2

    RonL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by CaptainBlack View Post
    It does in terms of the polylogarithm {\rm Li}_2

    RonL
    -Li_2(1+e^{x})-x\ln(1+e^{x})+\frac{1}{2}x^2?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

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

Search Tags


/mathhelpforum @mathhelpforum