Re: Can you help me to solve this Integrate using Mathematica ?
- To: mathgroup at smc.vnet.net
- Subject: [mg36244] Re: [mg36221] Can you help me to solve this Integrate using Mathematica ?
- From: BobHanlon at aol.com
- Date: Wed, 28 Aug 2002 04:16:04 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 8/27/02 3:33:59 AM, vpms at rc.unesp.br writes:
> I would like to know, if is possible to solve
>
> Integrate[(exp[-a/x])/(x^2-b^2),{x,0,infinity}] with
>
> a and b constant ( Real )
>
> using Mathematica.
>
Integrate[(Exp[-a/x])/(x^2-b^2),{x,0,Infinity},
GenerateConditions->False]//FullSimplify
Sqrt[-(1/b^2)]*((1/2)*Pi*Cosh[a/b] +
CosIntegral[a*Sqrt[-(1/b^2)]]*Sin[a*Sqrt[-(1/b^2)]]) +
(Cosh[a/b]*SinhIntegral[a/b])/b
FullSimplify[%, Element[{a,b}, Reals]]
(1/(2*b*Abs[b]))*(-2*b*CosIntegral[(I*a)/Abs[b]]*
Sinh[a/Abs[b]] + Cosh[a/b]*(I*b*Pi +
2*Abs[b]*SinhIntegral[a/b]))
Bob Hanlon
Chantilly, VA USA