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How to find the accurate numerical integration of highly oscillating functions involving ploylogs for example;

NIntegrate[
 PolyLog[2, E^(-2 I \[Pi] x)] PolyLog[2, 
   E^(-2 I \[Pi] Sqrt[321 + 712 x + 4 x^2])], {x, 1, 10^25}, 
 MaxRecursion -> 500]

The default global adaptive method above is currently not converging, is there any other integration strategy that coulf work for such functions.

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  • $\begingroup$ Are you really trying to integrate to 10^25? Or are you really trying to integrate to infinity? If so, do you know that the integral should actually converge? $\endgroup$
    – mikado
    Nov 20, 2022 at 22:37
  • $\begingroup$ I'm trying to integrate to 10^25 $\endgroup$
    – Smithy
    Nov 21, 2022 at 18:54

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