Results 1 to 6 of 6

Math Help - Stuck integrating with "e"

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    65

    Stuck integrating with "e"

    I'm stuck trying to solve this integral with "e". I am using the substitution method and made a sub, but cannot figure out how to apply it to this particular integral due to the sign of the exponent.
    Attached Thumbnails Attached Thumbnails Stuck integrating with "e"-stuckstep4.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2010
    Posts
    144
    Can't you say the following,

    \int (\frac{1}{4}e^{7x} + \frac{1}{e^{7x}})dx

    EDIT: Nevermind, this is incorrect, I'll edit this post if I find something else.

    Harish beat me to it!
    Last edited by jegues; October 9th 2010 at 10:50 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    4e^{-7x}+e^{7x} = \dfrac{4}{e^{7x}}+e^{7x}= \dfrac{4+e^{2(7x)}}{e^{7x}}

    \int \dfrac{dx}{4e^{-7x}+e^{7x}} = \int \dfrac{e^{7x}}{4+e^{2(7x)}} dx

    now let u = e^{7x} and complete
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2010
    From
    Athens
    Posts
    45
    Stuck integrating with "e"-img_0002.jpg
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2010
    Posts
    65
    Thank you this helped me solve it and was able to verify with Pandevil1990's scan.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member Hardwork's Avatar
    Joined
    Sep 2010
    Posts
    36
    Let \displaystyle u = e^{7x}, then \displaystyle \int \dfrac{dx}{4e^{-7x}+e^{7x}}\;{dx} \displaystyle = \frac{1}{7}\int\frac{dx}{(\frac{4}{u}+u)u}\;{du} = \frac{1}{7}\int\frac{1}{4+u^2}\;{du} . Let \displaystyle t = 2\tan{u} to get \displaystyle I = \frac{1}{14}\arctan\left(\frac{e^{7x}}{2}\right)+k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  2. Integrating "lumps" instead of "pieces"
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2010, 11:58 AM
  3. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  4. Stuck on "Reduced Row-Echelon Form is Unique" proof
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 20th 2009, 01:57 PM
  5. stuck on "e" and "ln" stuff
    Posted in the Algebra Forum
    Replies: 6
    Last Post: June 17th 2006, 07:35 PM

/mathhelpforum @mathhelpforum