The monster floor integral from the 2023 MIT Integration Bee finals

Here's the toughest integral from the 2023 finals. There's also a video for the entire finals:
• Solving all the integr...
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[@manstuckinabox3679]

Monkey in my brain: "sir I know you have a personal relationship with complex analysis, but I highly recommend you at least see the integral before sugge-"
Me: "wE cAn UsE CoNtOuR iNteGraTiOn"
edit: It doesn't work, I started it as a joke but went investigating the analytic continuation of the floor function, it extends quite horrendously.

[@maths_505]

🤣🤣🤣🤣🤣🤣🤣🤣🤣

[@manstuckinabox3679]

@@maths_505 on an unrelated side note, I think it could come in handy in boolean algebra, (the floor function of the unit circle gives either 0s or 1s

[@havalclaysoldier9688]

your u's and n's look so identical which makes harder to percieve the concept.

[@illumexhisoka6181]

Can you make a video about explaining how do you choose the method to solve an integral is there some hints is it experience do you just keep trying deferent methods

[@maths_505]

Definitely experience

[@themathsgeek8528]

Wow, this was absolutely mindblowing! The substitutions and techniques were amazing! Thanks for the video.

[@monikaherath7505]

How on earth did Luke solve this in under 4 minutes? What the flying fccck?!
I spent an entire hour trying to figure out how to break this down and gave up and started sobbing lol. Even after the video while I followed and understood each step mechanically I still have troubling understanding what the integral means intuitively or how to visualize it.
EDIT: Just rewatched this and the substitutions are just perfect wtf. Maths is mindblowing. It's amazing how a few tricks and substitutions can decompose a seemingly impossible integral into something manageable.

[@maths_505]

Thinking about how Luke did it is harder than the integral itself😂😂😂
Glad you liked the substitutions. It was all about doing making the floor function more hospitable.

[@hydra_brothers_gaming7881]

that was crazy long

[@mathiumlight]

Brooo, you could enter the square inside the sum and convert it to sum of cubes

[@MrWael1970]

Really monster integral. But has many cool ideas. Thanks for nice effort

[@quentinrenon9876]

What a beast! I wouldn't have seen that coming making it ever more satisfying! I wonder how you can see such things! Like this idea of doing a sub so that you can break the original integral into 2 two then reunite them etc... This is just so impressive great job!

[@maths_505]

Thanks mate....the trick is persistence

[@txikitofandango]

I hope Papa Flammy sees this

[@Risu0chan]

I died a little at 12:16

[@robertorascon4907]

Found this video ruclips.net/video/2-O6rYR6B4E/видео.html with the same solution as yours, even the variable names are the same, so I'm assuming procedure was taken from this video. Awesome work!

[@finmat95]

This is a real nightmare.

[@jawinfernandes9355]

great video !!!

[@Unidentifying]

suggestion: some crazy differential eqns

[@graydust]

What the app u using. I am a uni freshman i would to have st like this

[@AHMED_-123..]

What is the name of the program you use to write please😊

[@Unidentifying]

i believe you mean transformation n -> n-1

[@paarths.5281]

Knew there'd be something you can do with the bounds with this one. Honestly love that whenever floor functions come up you can turn everything into a regular summation. Also kinda surprised you stuck through for the entire problem. I would have gotten bored bu the time you made it to the (S+1)^2 term

[@paarths.5281]

By*

[@robertsandy3794]

Awesome, keep em coming

[@shanmugasundaram9688]

very interesting integral.

[@trambakphysik7]

I love this. Great work!❤

[@davode76166]

Great integral!

[@shreyanshmehta5810]

Second!!!!!

[@nicolascamargo8339]

Vaya

[@adhamkassem3058]

Thank you

[@sophie________]

I needed a breather after that too and I didn't even solve it