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A Nasty integral

  1. Apr 22, 2008 #1
    Any Ideas on how to Approach this one? ...

    [tex]\int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du[/tex]

    We have a [tex]sech(u)[/tex] and its derivative [tex]-tanh(u)sech(u)[/tex] and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

    Any Ideas? ...Thanks Heaps,
  2. jcsd
  3. Apr 22, 2008 #2
    Why would you think there exists a primitive which can be expressed as a combinaton of "simple" function?
  4. Apr 24, 2008 #3
    I doubt this will have a pretty substitution
    Maybe use the generalized binomial expansion...

    If that works you'll probably get a hypergeometric solution.
  5. Apr 25, 2008 #4
    Hello there

    I am not sure but I have few ideas and they might help.

    [1-secH(X)]^2 becomes -tanH(X)

    [cosX]^2 + [SinX]^2 = 1

    Dvide by [cosX]^2 and you will have

    1+[TanX]^2 = 1 over CosX^2 which [SecX]^2
    1- [SecX]^2 = -[tanX]^2

    The root of the first one is -[tanX] if I am not mistaken.
    The Second one becomes [-SecH(x)]^2

    This works if H is not a constant.
  6. Apr 25, 2008 #5
  7. Apr 25, 2008 #6
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