# The integrand has evaluated to Overflow, Indeterminate or Infinity

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

 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

• 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? Nov 22 '21 at 16:44
• @Bill made the correction but error still persists Nov 22 '21 at 17:07
• @MichaelE2 thank you very much!, will try searching for suitable substitution Nov 22 '21 at 17:08
• @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. Nov 26 '21 at 6:49