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Mathematica says that the following complicated integral is infinity, which is reasonable:

    Integrate[((11/10)^(2/5)*Abs[t2/t1]^(1/5)*
    Abs[-t1 + (10/11)*(-1 - t1 + t2)]^(1/5))/
     (Abs[t1 - t2]^(2/5)*Abs[-1 - t1 + t2]^(2/5)*
    Abs[-t2 + (10/11)*(-1 - t1 + t2)]^(1/5)), 
   Element[{t1, t2}, 
  ImplicitRegion[t2 < (10/11)*(-1 - t1 + t2) < t1 < 0, {t1, t2}]]] 

I want to understand why the result is $\infty$. I used Trace command, but it gives a non-useful result as follows:

enter image description here

How can I get more detailed steps?

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4
  • $\begingroup$ Can you post the InputForm of your input? Your code is not readable as is. Trace is not really useful for finding flow of logic of a function. Hard to read and figure what it all means. $\endgroup$
    – Nasser
    Oct 31, 2021 at 12:45
  • $\begingroup$ @Nasser Sure, I edited the question. If Trace is not useful, then what are other standard options? $\endgroup$
    – Laplacian
    Oct 31, 2021 at 12:48
  • 2
    $\begingroup$ There are better traces and use option TraceInternal->True $\endgroup$
    – RungeC
    Oct 31, 2021 at 12:53
  • $\begingroup$ If you want to know why the improper integral under consideration diverges, then the integration of the term Abs[t2/t1]^(1/5) over the unbounded region of the integration (see Reduce[t2<(10/11)*(-1-t1+t2)<t1<0,Reals]) causes it. $\endgroup$
    – user64494
    Oct 31, 2021 at 17:13

1 Answer 1

2
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  1. Use Trace:
Trace[(* integral *), TraceInternal->True]

You can find some better trace(more human readable) here. Note in most cases, sizes of trace results are very large(hundreds of MB). So it's not a good idea to view them in your notebook. Try to open them in some text editor.

  1. Internal debug messages of Integrate.
Block[
    {
         Internal`Integrate`debugSwitch = 10,
         $Output = OpenWrite[
              (*log file location*)]
     }
     (*integral*);
     Close@$Output;
];
Import[(*log file location*), "Text"]

But notice since Integrate has code(i.e., has kernel definitions) and we can't view comments in source codes through public definitions(i.e., DownValues), this log may be very hard to understand...

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