I Tried ISI Integration Bee 2026 Finals Round!

追加: 2026-05-31

[00:00:00]Wasabi. You guys, it's time for the finals round of ISI integration B 2026.

[00:00:08]About time. And if you remember from the previous ones, holy macro.

[00:00:16]They are they can they can be both brutal and interesting. Um but the finals round is like the one that I'm just number one most terrified about.

[00:00:29]just just knowing how the prom writers are and their style and it's it's just oh I'm a I'm a bit terrified but at the same time I'm really really excited to what tricks they're going to come up with. So let's go ahead and start with the first integral what they got.

[00:00:52]Okay, this see as soon as I see like 01 polomials and ln of x at the bottom, I think about that famous fineman technique.

[00:01:02]But is it really what that is?

[00:01:07]We better find out right now. So, okay, we're going to try to factor this as much as we can.

[00:01:17]Kind of see what they have. No. If I shove 1 - x in, I get like 1 - x cub.

[00:01:26]But then I have 1 - x^2 which is equal to 1 - x of 1 - x ^ of well the way I see this is let alpha should probably stop doing that. Let a= x cub then what we have is like this, right?

[00:01:49]And that is like what? 1 + a 1 + a squar.

[00:01:56]So we need to do this one. Oh no. Plus plus x^ 6. Uh the shade is a bit different. I don't know why.

[00:02:09]Just ignore that. Um it's kind of bugging me actually. I don't know why. All we got to do now is just kind of distribute it. I'm hoping I did all of that correctly. Okay. So now I want you to realize that x to the power of a minus x^ of b ln x this is equal to like ln of a over oh sorry ln of a + 1 over b + one.

[00:02:46]Okay. So what we have here all this all over ln of x. Okay, this is literally what we have.

[00:02:57]So then this means that we have ln of let's see that's going to be like ln of one all over ln of 2, right? uh ln of 4 over five ln of 7 over 8 ln over of uh 10 over 11.

[00:03:27]So we must have like what? This is two.

[00:03:30]This is now two. So have two 2 and two.

[00:03:35]This is now two. So we have like ln of 7 over 22.

[00:03:40]Is that what we got?

[00:03:44]So our answer is ln of 7 over 22. I'm going be so mad if it's flipped. Okay, they did fineman. Oh my god, it is flipped. What did I What? Yeah. No, but this is correct.

[00:03:58]Wait, so why was it Wait, why was mine's flipped then? Cuz I got one - x. Yes, it's two.

[00:04:06]I got four.

[00:04:11]Wait. Okay. So, where where did the negative come from?

[00:04:14]y - x I don't get it. Where did the negative come from? What the hell?

[00:04:23]What?

[00:04:25]Huh? What did I do wrong? Okay. 1 - x 1 + x cub 1 + x^ 6.

[00:04:34]Uh 1 - x cub. Yeah. No, that's correct.

[00:04:40]So, I'm not missing a negative here.

[00:04:42]What? So, why is it flipped? Because they got the exact same thing as I got.

[00:04:47]Ah, yeah. There we go. See, we get a negative number. Yeah. So, this this should have been a negative number.

[00:04:54]Yeah. So, it it should have been flipped. I think this was a typo. The answer was indeed a typo. Yeah. So, it should be 7 over 22.

[00:05:05]Okay. I was I'm like I'm going crazy.

[00:05:07]I'm like, what did I do wrong? I swear to God. I swear it was it's it's negative. I swear.

[00:05:15]But okay. So, I think this this they accidentally flipped it the other way around. Gotcha.

[00:05:22]Okay. First integral done. All right.

[00:05:24]So, we got I got one finals integral done. Correct. Awesome. Let's go. All right. Next one. I swear if you pull something, I'm going be so mad. What is this?

[00:05:39]Of course. Of course you come up next.

[00:05:42]God damn you.

[00:05:44]What is this?

[00:05:47]What the hell?

[00:05:50]Huh? Oh, you know what this reminds me of? Hold on. Wait. I'm getting flashbacks. This This integral reminds me of um there's a very There's a sneaky Olympiad line here. It's like a It's crap. I think it was from like Lawrence Glasser.

[00:06:09]I think the guy the the the guy who made Glass's master theorem. Uh he he did like this a cool it's like a very awkward u substitution. It's similar like this, but I forgot how he did it.

[00:06:24]It's like um when you have it it is it's not even like improper. It's like some some bound and you have like a function of some sort and it's like an irrational expression like this and it's like a cool use of that like simplifies everything. It makes it look nicer but I don't remember how to do it. Um but that's what this is kind of giving me that vibe. Oh, wait a minute. Wait a minute. I have an idea.

[00:06:55]Maybe not. Maybe not. I was going to isolate x+ one, but it's going to give me like I don't know. I I don't know if I want to deal with something like that.

[00:07:03]I don't know if I want to isolate x+ one. I'm too lazy.

[00:07:08]Um why you got to do this to me? Okay, let a alpha= x + 1. Then we get uh zero of alpha^ 2 minus u alpha - 2. And this is going to give me x + one equals e. I don't know if I want to do this.

[00:07:41]Okay. Okay. If I plug in zero. God, no.

[00:07:52]I don't know if I want to do this, but I don't think I got a choice.

[00:07:57]I don't think I got a choice. So, oh, that's disgusting. You're evil for putting it as 2026 and then the u square root of blah blah blah. But no one cares about that because that's that's an odd function. So now what we have is 1/4 of u ^ 206 of 2 u 2 + 8. That's actually a lot nicer than I thought. So this the radicals the radicals don't cancel out. Okay. Oh, thank heavens. I'm I'm assuming I did this correctly. I hope I'm doing this correctly, but I will cry if I got everything wrong. Oh, please tell me that's the answer. I didn't think that would come off very nicely. The symmetry really helped me out. All right. Ew.

[00:08:52]The involution, huh?

[00:08:57]What? What did you Oh no.

[00:09:04]What in the functional equation are you do?

[00:09:08]Oh, that's actually kind of sneaky.

[00:09:13]Oh my god. Yeah, because F of F. Oh, no way.

[00:09:19]Then with that, you can add it up, bro.

[00:09:24]There's no what?

[00:09:27]One over 2027.

[00:09:30]Huh?

[00:09:32]What?

[00:09:34]That's I'm pretty I don't know if my answer is the same thing. I highly doubt it is, but let me check just cuz how funny would it be if it was actually the I highly doubt it actually. I I doubt it would be the same answer, but yeah, I know it would not be the same thing. Would not be the same thing. What the hell? Okay, maybe I did my you substitution incorrectly then. Maybe that's what it is. I think I just did my usub incorrectly.

[00:10:04]I was kind of proud. I was like, damn. I thought I would get that. But no, I was wrong. I was wrong. Yeah, this is way too sneaky. This was This is just This This is slick. I would have never thought of this.

[00:10:19]Holy hell. The functional equation trick was just This is evil. This is beyond evilness. Holy crap. But at the same time, like this was pretty cool.

[00:10:32]Like, holy This is just this is cool and evil at the same time. Of course, it's got to be from the Rahul.

[00:10:40]Holy hell. All right, hit me with the other one. Let's go.

[00:10:46]Oh, no. Don't give this to me.

[00:10:52]Why would you? Is this from MIT?

[00:10:55]Oh my god. I'm not doing this. This is from a Putnham problem. It's literally an integral created from a Putnham problem. It's that stupid telescoping pi product with the cubix.

[00:11:07]I'm I don't want to do this. I don't I don't know how to do this. This this is it's a math Olympia oriented integral.

[00:11:15]I'll just I'll show it to you. This is from MIT. Um it's it's not even you just pretty much turn it into Yeah, it's a simple integral and all it is is you're just left with this. Where is it? This.

[00:11:28]That's it. That's all it is. And then it's just this is literally a Putnham problem.

[00:11:34]It's it's it's it's from a Putnham pro a Putnham exam. I don't remember what year it is, but it's a famous Putnham problem where it's like a pie telescoping pie.

[00:11:46]Yeah. This this thingamajig.

[00:11:49]Yeah. Ew. They No, thank you.

[00:11:55]Yeah. you. It's It's very tricky to find the telescoping product. Yeah.

[00:12:04]Yep. This it's it's weird. It's very weird.

[00:12:12]I'm not that comfortable with like algebra olympiad. So, it's like it's kind of like hard for me to even like comprehend like what is going on. Yeah.

[00:12:22]I only know up to like here, right?

[00:12:24]Turning it into a sum was the easiest part. The main problem is just solving it. Computing the sum is just an annoyance.

[00:12:34]Expanding it. Yeah, expanding. Oh, that's it. Dang. That's it. Oh, disappointing. How could you throw an MIT integral last? Dang. This was cool.

[00:12:48]This was really cool. Uh, I'm sad I didn't get that correctly, but this this idea, the intention is very very sneaky.

[00:12:56]I would have never thought of this. This was a very cool sneaky line. Um, this one was just fun.

[00:13:04]This one was kind of fun. Dang, that was a short finals. I thought it was more, but no, it's just three integrals, which makes sense. Which makes sense. I think two I think finals was I'm assuming it was like best out of three. So, uh, but this was evil. This was evil. I don't know how you guys How do you guys not have tiebreers? I just realized.

[00:13:24]Holy Uh, but yeah. Well, I mean, that was it.

[00:13:30]That was Yeah, that's that that was kind of short a little bit, but yeah, I apologize. Yeah, I don't know how to do this. I know how to turn into a sum, but that's that's about it. Oh, disgusting MIT integrals. Uh, overall this integration me was it was fun.

[00:13:49]Rahul is like the the evil prom writer here.

[00:13:54]I swear to God, it's always Rahul always gets me. But man, these the problems are actually it's I don't know how to explain it. It's like these problems, they're like it's like at the same time bashy, but also like gets you hooked into like the integral. Like it makes you like like when you see these integrals like this, for some reason it makes you like get hooked into like trying it no matter how like even like this. Like I'm surprised you got me hooked into uh what was it? This. I can't even believe I even attempted this and like almost nearly solved it. Sadly, I did not. It was too many too much going on. This was bashy. But at the same time, it made you realize like, huh, wait a minute. There's something sus. You see, Rahul is evil, but Rahul at least at least you had standards. You at least you kind of it's not like bashing for the sake of bashing. Okay, maybe a little bit. This one was kind of bashing for the sake of bashing, but the others was kind of like it was pretty slick. Um, holy crap. Yeah, this was Yeah, bashy, but at the same time, it makes you like interested in trying it, you know, and that's that's not very easy to kind of do as a prom writer cuz a lot of contestants would just be like, "Yeah, I don't want to try this." But these integrals, they're like at least you you made it more interesting. This was just disgusting. I don't ever want to try this. But that's just bash. But the rest was like uh like this one. I can't believe I got hooked into this as well.

[00:15:38]Like I don't know how you're doing it.

[00:15:40]But uh yeah, and this too.

[00:15:46]And this. Yeah. I can't believe I even solved this. That I can't even believe I figured this one out. But yeah, the problems were very fun. I actually enjoyed this integration B a lot more than I thought. Um, yeah, and including the qualifiers, too. So, yeah, that's it. That's ISI integration B 2026. I'm excited for like next year's or the other problems. So, that was that was very fun.

[00:16:16]Huge props to them. Awesome. All right.

[00:16:19]Huge thanks to those who kind of uh showed me this. This was a really fun integration be I'm really glad to try this out. Uh yeah, thank you guys so much for watching and I'll see you guys in the next video. See you.