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Math Help - integration of exp(-sinh(x))

  1. #1
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    integration of exp(-sinh(x))

    I have been working on some perturbation (asymptotic) methods work and I have ran into an issue... I can't seem to figure out a way to integrate:
    exp(-sinh(x))
    I tried using u substitution and that doesn't work (unless i did something wrong). Could anyone shed any insite such that i can solve this integral?

    Thanks

    MT
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  2. #2
    Super Member redsoxfan325's Avatar
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    \int e^{-\sinh x}\,dx can not be expressed in terms of elementary functions. I believe the best you can do is a numerical approximation.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by robotENGR View Post
    I have been working on some perturbation (asymptotic) methods work and I have ran into an issue... I can't seem to figure out a way to integrate:
    exp(-sinh(x))
    I tried using u substitution and that doesn't work (unless i did something wrong). Could anyone shed any insite such that i can solve this integral?

    Thanks

    MT
    Now if it was \int e^{-\text{arcsinh}(x)} dx we'd be able to get somewhere. Are you sure it isn' this?
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