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Math Help - Integral of exp(-a*m)*sech^{1/m}(a*m) dm

  1. #1
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    Integral of exp(-a*m)*sech^{1/m}(a*m) dm

    Hi,

    I would like at least some hints to compute the following integral :

     \int_0^\infty exp(-ax) \text{cosh}^{-1/x}(ax) dx

    As a known result we have :
    \lim_{x->0} \text{cosh}^{-1/x}(ax) = 1

    So the function should behave well and be integrable but mathematica gives no anwser for it...

    Can somebody help ?

    Thanks

    Alexis
    Last edited by AlexisM; August 1st 2010 at 07:55 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by AlexisM View Post
    Hi,

    I would like at least some hints to compute the following integral :

     \int_0^\infty exp(-a*x) \text{cosh}^{-1/x}(a*x) dx

    As a known result we have :
    \lim_{x->0} \text{cosh}^{-1/x}(a*x) = 1

    So the function should behave well and be integrable but mathematica gives no anwser for it...

    Can somebody help ?

    Thanks

    Alexis
    Can you provide some background, why you need this integral (the problem it is part of ...) what if any level/ quality of approximation would be acceptable for the integral, ...

    CB
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