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Integration of hyperbolic functions

  1. Sep 8, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int cosh(2x)sinh^{2}(2x)dx[/tex]

    2. Relevant equations

    Not sure

    3. The attempt at a solution

    This was an example problem in the book and was curious how they got to the following answer:

    [tex]\int cosh(2x)sinh^{2}(2x)dx = [/tex] [tex]\frac{1}{2}[/tex][tex]\int sinh^{2}(2x)2cosh(2x) dx[/tex]

    = [tex]\frac{sinh^{3}2x}{6} + C[/tex]

    My issue with this problem is I don't understand what happened to the [tex]2cosh(2x)[/tex]. It relates to [tex]sinh^{2}(x)+cosh^{2}(x)[/tex] but that only equals 1 in normal trig, not hyperbolic. Thanks in advance.

    Last edited: Sep 8, 2010
  2. jcsd
  3. Sep 8, 2010 #2


    Staff: Mentor

    Hyperbolic trig identities would be very relevant.
    For some reason, your LaTeX wasn't showing up correctly. I fixed it by removing several pairs of [ tex] and [ /tex] tags.
    Tip: Use one pair of these tags per block.
    The integration was done using an ordinary substitution, u = sinh(2x).
  4. Sep 8, 2010 #3
    Ya I just realized that if I set u= sinh(2x) then du=2cosh(2x) dx then substitute from there. Thanks

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