Difficulty in solving an integral in Mathematica

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SUMMARY

The forum discussion centers on solving a complex integral using Mathematica, specifically with the function NIntegrate. The user reports issues with convergence for values of t greater than 42, leading to results that are unreasonably small, such as <10^-700. The integral involves parameters b, c, g, and s, and the user is advised to adjust the desired accuracy settings in Mathematica to achieve better results.

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This discussion is beneficial for mathematicians, researchers, and students working with numerical integration in Mathematica, particularly those facing convergence issues in complex integrals.

k0st123
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Hello,

I have to solve the following integral in Mathematica but although I don't get any mistakes the value I get is <10^-700 which can't be right!

For the following values

b=0.052868
c=0.998047
g=0.00762712
s=0.902416

I have to solve the following:

Fx = Table[NIntegrate[(Exp[-t*x^2/g]/x^3)*(Sin[x] - x*Cos[x])*(b*x*Sin[x]*Cos[s*x] - (c*Sin[x] - x*Cos[x])*Sin[s*x])/((c*Sin[x] - x*Cos[x])^2 + (b^2*x^2*Sin[x]^2)),{x, 0, Infinity}],{t, 13, 100, 1}];

Could you possibly help me?I guess the problem is the exponential part which is really huge.This problem has been bothering me for a couple of weeks now!

Thank you guys

k0st123
 
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It works fine up to t = 42. For t=43, the integral doesn't converge to the prescribed accuracy. You need to tweak the desired accuracy.
 

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