Results 1 to 9 of 9

Math Help - Integrate cosh x/(3 sinh x +4)

  1. #1
    Member
    Joined
    May 2010
    From
    WI - USA
    Posts
    129

    Integrate cosh x/(3 sinh x +4)

    Given

     <br />
\int{\frac{cosh(x)}{3 sinh(x)+4}}<br />

    I come up with

    let u=sinh(x), du=cosh(x)

    \int{\frac{du}{3u+4}}

    So

    \frac{1}{3}\int{\frac{du}{u}}+4

    And

    \frac{1}{3} sinh(x)+4x+C

    So, how many rules did I violate or otherwise offend with this one?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    I never worked with sinh nor cosh but I can tell you this:

    \frac{1}{x+1} \neq \frac{1}{x} + 1

    What you need to do from

    \int{\frac{du}{3u+4}}

    is to use ln.

    If you differentiate the denominator, you get 3, so:

    \int{\frac{du}{3u+4}} = \frac{1}{3} (ln(3u+4)) + c

    From there, you can substitute back.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Personally, I will substitute u=3sinh(x)+4 ..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2010
    From
    WI - USA
    Posts
    129
    Ok...

    Then it should look something like...

     <br />
\int{\frac{cosh(x)}{3 sinh(x)+4}}<br />

    let

     <br />
u=3sinh(x)+4<br />
    <br />
du=3cosh(x)<br />

    So...

     <br />
\int{\frac{\frac{1}{3}du}{u}}<br />

    And...

     <br />
\frac{1}{3}\int{\frac{du}{u}}<br />

    And...

    \frac{1}{3}u+C

    So...

    \frac{1}{3}(3sinh(x)+4)+C

    And finally...

     <br />
sinh(x) + \frac{4}{3} +C<br />
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    You seem to have forgotten your integrations...

    \int \frac{1}{x} dx = ln(x) + c

    or;

    \int \frac{f'(x)}{f(x)} dx = ln(f(x)) + c
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Quote Originally Posted by Unknown008 View Post
    You seem to have forgotten your integrations...

    \int \frac{1}{x} dx = ln{\color{red} |}x{\color{red} |} + c

    or;

    \int \frac{f'(x)}{f(x)} dx = ln{\color{red} |}f(x){\color{red} |} + c

    ..
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Quote Originally Posted by General View Post
    ..
    Yes, but in my education system, they do not put the absolute symbols, and we are not given marks for them in the exams, so I tend to forget those...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    May 2010
    From
    WI - USA
    Posts
    129
    Doh...

    How about this then...
     <br />
\frac{1}{3}ln|3sinh(x)+4|+C<br />

    I just reviewed logarithmic differentiation and integration. I can't believe I missed that.

    I don't recall seeing the absolute value being ephasized in my book either. Ah, nevermind, there it is.

     <br />
\int{\frac{dx}{x}}= ln|x|+C<br />
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Quote Originally Posted by MechEng View Post
    Doh...
    How about this then...
     <br />
\frac{1}{3}ln|3sinh(x)+4|+C<br />
    Correct..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sinh(x) and cosh(x)
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 13th 2011, 09:37 AM
  2. INT (sinh t. cosh 2t) dt
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 16th 2010, 08:34 AM
  3. Replies: 1
    Last Post: May 26th 2010, 01:30 PM
  4. Help with sinh and cosh
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: October 27th 2009, 10:57 PM
  5. cosh and sinh
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 24th 2007, 09:47 PM

Search Tags


/mathhelpforum @mathhelpforum