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