RE: Can you help me to solve this Integrate using Mathematica ?
- To: mathgroup at smc.vnet.net
- Subject: [mg36248] RE: [mg36221] Can you help me to solve this Integrate using Mathematica ?
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 28 Aug 2002 04:16:08 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Valdeci,
It appears that the integral will not converge if b is real. Mathematica
gives...
Integrate[Exp[-a/x]/(x^2 - b^2), {x, 0, Infinity}]
If[Re[a] > 0 && Arg[b^2] != 0, (1/2)*Sqrt[-(1/b^2)]*
(2*CosIntegral[a*Sqrt[-(1/b^2)]]*
Sin[a*Sqrt[-(1/b^2)]] + Cos[a*Sqrt[-(1/b^2)]]*
(Pi - 2*SinIntegral[a*Sqrt[-(1/b^2)]])),
Integrate[1/(E^(a/x)*(-b^2 + x^2)), {x, 0, Infinity}]]
If b is Real then Arg[b^2]==0 and Mathematica doesn't solve it. Let's define
a function that allows us to test specific values of a and b.
f[a_, b_][x_] = Exp[-a/x]/(x^2 - b^2);
Integrate[f[2, 3][x], {x, 0, Infinity}]
Integrate::"idiv" : "Integral of 1/(E^(2/x)*(-9 + x^2)) does not converge on
\
{0, Infinity}."
But if we use an imaginary value for b...
Integrate[f[2, 3I][x], {x, 0, Infinity}]
%//N
(1/6)*(2*CosIntegral[2/3]*Sin[2/3] +
Cos[2/3]*(Pi - 2*SinIntegral[2/3]))
0.254022
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Valdeci Pereira Mariano de Souza [mailto:vpms at rc.unesp.br]
To: mathgroup at smc.vnet.net
Dear Group
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.
Thankfully,
Valdeci Mariano
*********************************************************************
Valdeci Mariano de Souza
Master´s Degree of Applied Physics - Unesp/Rio Claro - State of São
Paulo - Brazil
Laboratory of Electrical Measurements
email : vpms at rc.unesp.br or valdecimariano at bol.com.br
phone : ( 0XX19 ) 526 - 2237
*********************************************************************