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I'm tasked with investigating the decay rate of clusters over a period of time, the decay rate is given by ; details of integral

 Clear[x]
G[t_?NumericQ] := NIntegrate[10^16*(((x-2.82)^17)/((x+.021)^20))*(\[ExponentialE]^(-10^16*(((x-2.82)^17)/((x+.021)^20))*t)),{x,0,\[Infinity]}]

However when I try to evaluate, I receive the error that the integrand has evaluated OverFlow, Indeterminate or Infinity within boundaries {0.333,0}. Could anyone please suggest an answer to solve this issue? Sorry if this seems elementary, my coding skills are still basic

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  • $\begingroup$ Compare the logarithm of your exponential factor with the logarithm of the maximum number: (-10^16*(((x - 2.82)^17)/((x + .021)^20))*t) /. t -> 1 /. x -> 1/2. and Log@$MaxNumber. You're well outside the computable domain here. Maybe you can transform the integrand? $\endgroup$
    – Michael E2
    Nov 22 '21 at 16:44
  • $\begingroup$ @Bill made the correction but error still persists $\endgroup$
    – Trevz
    Nov 22 '21 at 17:07
  • $\begingroup$ @MichaelE2 thank you very much!, will try searching for suitable substitution $\endgroup$
    – Trevz
    Nov 22 '21 at 17:08
  • $\begingroup$ @MichaelE2 instead of integrating to infinity i'm trying to integrate to a lesser value. for example 20 , values for t will be really low >0.001. somehow the code still runs the same error,the value of the expression is below the max number for these values ; (10^15*(((x - 2.82)^17)/((x + .021)^20))*-10^16*(((x - 2.82)^17)/((x + .021)^20))*t) /. t -> .001 /. x -> 0. $\endgroup$
    – Trevz
    Nov 26 '21 at 6:49

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