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

• Jul 27th 2010, 03:53 AM
AlexisM
Integral of exp(-a*m)*sech^{1/m}(a*m) dm
Hi,

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

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

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

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

Can somebody help ?

Thanks

Alexis
• Jul 29th 2010, 04:43 AM
CaptainBlack
Quote:

Originally Posted by AlexisM
Hi,

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

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

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

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