Results 1 to 4 of 4

Thread: Integrate

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    31

    Integrate

    the intergal of 1/(e^(2x)-1) dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Infophile's Avatar
    Joined
    May 2009
    Posts
    56
    Hello,

    $\displaystyle u=e^{2x}$ and $\displaystyle du=2u.dx$.

    So $\displaystyle \int \frac{1}{1+e^{2x}}dx=\frac{1}{2}\int \frac{1}{u(u-1)}$

    But $\displaystyle \frac{1}{u(u-1)}=\frac{1}{u-1}-\frac{1}{u}$.

    Hence $\displaystyle \frac{1}{2}\int \left(\frac{1}{u-1}-\frac{1}{u}\right)=\frac{1}{2}\left(\ln(u-1)-\ln(u)\right)+C$

    Therefore a primitive is $\displaystyle \color{blue}\boxed{x\mapsto \frac{1}{2}\ln\left(\frac{e^{2x}-1}{e^{2x}}\right)}$ or still $\displaystyle \boxed{x\mapsto \frac{1}{2}\ln(2sh(x))}$

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    Quote Originally Posted by tiga killa View Post
    the intergal of 1/(e^(2x)-1) dx
    $\displaystyle \frac{1}{e^{2x}-1} = \frac{1 - e^{2x} + e^{2x}}{e^{2x} - 1} = \frac{e^{2x}}{e^{2x}-1} - \frac{e^{2x}-1}{e^{2x}-1} = \frac{e^{2x}}{e^{2x}-1} - 1$

    integrate the last expression
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member Infophile's Avatar
    Joined
    May 2009
    Posts
    56
    Yes, why not, it's faster.

    Hello skeeter
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrate 3 e^x
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jun 9th 2010, 01:16 PM
  2. how to integrate this ??
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Aug 9th 2009, 08:14 PM
  3. Integrate
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Apr 28th 2009, 07:54 PM
  4. How to integrate x^x?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Apr 25th 2009, 07:51 PM
  5. Integrate
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Apr 15th 2009, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum