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Aug 9, 2022 at 16:05 comment added Michael E2 @Ji'anLi Also, I'm using V13.1. Integrate[] is updated probably in every new version of Mathematica. If you're using a different version, it might explain why the GenerateConditions -> False version takes more than a few seconds.
Aug 9, 2022 at 16:02 history edited Michael E2 CC BY-SA 4.0
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Aug 9, 2022 at 15:59 comment added Michael E2 @Ji'anLi You're welcome. I would say that anything that takes 1100 sec. on a modern computer is doing a lot. The answer I linked shows how to get more information, but I would expect the output to be hundreds of pages. Most of the output will be impossible to understand without being familiar with the internal code. I'm not, and I wouldn't look into this any farther. I'd be satisfied with finding the Csc[5 t] factor above and thinking that's leading to difficulties.
Aug 9, 2022 at 15:53 history edited Michael E2 CC BY-SA 4.0
Clarification
Aug 9, 2022 at 15:45 comment added Ji'an Li Thanks for help (^_^) ` Integrate[ Cos[2 t] Cos[3 t] Cos[4 t] Cos[5 t] Sin[2 t] Sin[3 t], {t, 0, 2 Pi}, GenerateConditions -> False] ` this code still needs a long time, and I aborted it after a minute wait. The debugging techniques is really helpfull, I think I need to take a good look at it, so that to figure out what happened during the points process
Aug 9, 2022 at 15:23 history answered Michael E2 CC BY-SA 4.0