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

    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?

  • $\begingroup$ 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

  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.
         Internal`Integrate`debugSwitch = 10,
         $Output = OpenWrite[
              (*log file location*)]
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...


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.