an Integrate question

• To: mathgroup at smc.vnet.net
• Subject: [mg58812] an Integrate question
• From: "Antonio Carlos Siqueira" <acsl at dee.ufrj.br>
• Date: Tue, 19 Jul 2005 04:10:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear MathGroup
I am trying to find an analytical answer for an integral such as:
(1) Integrate[Exp[-m Sqrt[x^2+b^2]]/(x+Sqrt[x^2+b^2]),{x,0,Infinity}]
where b and m can be Complex.
I know that
(2) Integrate[1/(E^(m x)*(x+Sqrt[x^2+b^2])),{x,0,Infinity}] has an
analytical answer although Mathematica cannot find and it is:
(3) Pi/(2 b m) (StruveH[1,b m]-BesselY[1, b m]) - 1/(b^2 m^2)
The response (3) checks with the answer I get from NIntegrate even when
b and m are complex.
So I was wondering if any of you guys could help me figure out whether
or not an analytical result for (1) is possible.
BTW I can get the numerical results in (2) using NIntegrate.
So any suggestions or comments on how I can solve (1) are highly
appreciated.
I forgot to say, I am using Mathematica 5.1 on windows.
Nice Regards
Antonio

```

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