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Hyperbolic substitition question:

  1. Aug 19, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int \!\sqrt {1+{v}^{2}}{dv}[/tex]

    2. Relevant equations

    Maple tells me that I have to throw in an arcsinh into the solution some how.

    3. The attempt at a solution

    I've tried substituting with tan(x) but that got me no where and from the solution I'm given:

    [tex]1/2\,v\sqrt {1+{v}^{2}}+1/2\,{\it arcsinh} \left( v \right)[/tex]

    I'm not sure how you get the first term and I know that arcsinh(v) is the integral of 1/sqrt(1+v^2)
  2. jcsd
  3. Aug 19, 2007 #2

    matt grime

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    Homework Helper

    If the answer involves inverse sinh, why not put sinh (or cosh or tanh) into the equation?
  4. Aug 20, 2007 #3

    Gib Z

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    If you don't exactly like arcsinh, just rewrite sinh in terms of the exponential function and find its inverse. This shows you that arcsinh is just a fancier way of writing: [tex] \log_e (x + \sqrt{x^2+1})[/tex]

    Edit: P.S. u= tan x was a good idea :) Go along with it.
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