# See how Mathematica computed the integral

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:

How can I get more detailed steps?

• 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. Oct 31, 2021 at 12:45
• @Nasser Sure, I edited the question. If Trace is not useful, then what are other standard options? Oct 31, 2021 at 12:48
• There are better traces and use option TraceInternal->True Oct 31, 2021 at 12:53
• 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. Oct 31, 2021 at 17:13

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[
{
InternalIntegratedebugSwitch = 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...