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Finding Indefinite Integral of a combination of hyperbolic functions

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Compute the following:

    [itex] \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx [/itex]


    2. Relevant equations
    [itex] \int cosh(x)\,dx = sinh(x) + C [/itex]


    3. The attempt at a solution
    I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made [itex] u = tanh(\frac{x}{2}) [/itex] and I had no clue how I am supposed to know to do that.

    Any advice on where to start is greatly appreciated.
     
  2. jcsd
  3. Sep 9, 2012 #2
    I solved this problem after realizing that [itex] cosh^2(x) - 1 = sinh^2(x) [/itex]. This allowe me to split make it [itex] \int coth(x)csch(x)\,dx [/itex], and then I could use another identity to set that equal to [itex] -csch(x) + c [/itex]
     
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