A Vaary Noice 3rd Place Match! [Bonn University Integration Bee 2026]

Añadido: 2026-06-02

[00:00:00]What's upabi you guys? Silver here.

[00:00:02]We're going to try the third place match from Bone University integration be 2026.

[00:00:08]And now uh I think so far from all these past integrals, they're not as hard. So I'm not expecting monstrous integrals unless unless I'm mistaken. Unless they just start throwing some brut brutality at us in in this level. I don't know. We we will the world may never know. uh or at least for me. But oh boy, I am excited for some cool some cool wild card integrals that they might throw at us. So, let's begin this. What? Huh?

[00:00:46]Oh god. Never mind. Nothing's easy at this point. Oh well, let x let you equal x square, of course. But I'm assuming this is like this partial fraction is nasty. Uh, oh god, this part.

[00:01:06]Yeah. No. So, this partial fraction is nasty. Let's Let's see why. Immediately, we can simplify this, right? Start small. Let's start small. There's nothing wrong with that. So 1 / two we get u u + 3 uh u ^2 - 1 and u + 1. Okay.

[00:01:30]Yikes. Um dang. I honestly don't want to do partial fractions. Uh there has to be some way around this. I Please tell me there's a way around this. I hope this is not pure. I really hope you didn't throw us a pure partial fractions. Like, this is a disgusting way to do third place match. Like, to give us a textbook problem like this. Like, come on. Come on. Wait a minute. I feel I realize if you do U + 1, U + 2, and then minus 2.

[00:02:04]I mean, I I feel like this wouldn't be as bad.

[00:02:10]And the reason why I say this is because Oh no. But then uh you can't really dodge that. Oh god.

[00:02:24]Ew.

[00:02:26]Fine. I'll do it your way.

[00:02:35]All right. What do they got? What on earth do they got?

[00:02:40]Um, one over 24 len of two.

[00:02:44]What?

[00:02:46]Where? Where the len of three stuff go?

[00:02:50]You got len of three. Oh my god, it's four. I miscounted.

[00:02:58]God damn it. Oh my god, I miscounted.

[00:03:02]So the one and then this was one. A. Oh my god. So now U + 3 is equal to Oh my goodness grief.

[00:03:17]This would have been so much nicer. God damn it. u ^2 - 1 + u - 1.

[00:03:24]Oh my god.

[00:03:26]Yeah. And then if you let u equal to zero then this is 0 = um 1 and then plus uh a.

[00:03:38]So a would have been a would equal to zero. Yeah. Oh my god, I miscounted.

[00:03:47]All right, let's just let's just go.

[00:03:49]Let's just go. That's actually a lot nicer. It wasn't actually that nasty. If it was that case, then yeah, this would this was actually not as nasty, right?

[00:03:59]If it was this case, right? If it was the one that I had, then yeah, it would have been nasty. But no, it was it wasn't actually that nasty. Damn it. Oh jeez.

[00:04:12]Okay, next. Just next. Let's just go.

[00:04:14]I'm sad. I'm sad. Modest but beautiful.

[00:04:18]This is pretty modest. Um because we have sign and sign plus one, right? Just do one. Just do plus one minus one. Tool easy.

[00:04:27]Tool easy.

[00:04:30]Is that what you guys got? Yeah. Okay.

[00:04:33]Too easy. Too easy. What's next?

[00:04:38]Oh god. Oh, tricky triggs.

[00:04:43]Okay. Oh god. What on earth have you given us? Oh no. But these are different.

[00:04:51]Wait a minute. Let's let's simplify this. Right?

[00:04:56]If we factor out sin of x of 2 cosine of x, then what we have is s cosine^ square over s. So that's like x coseant of x minus and then we have ln of sin of x sin of x.

[00:05:24]Huh interesting.

[00:05:28]Can we turn this into e to the ln of sin of x times ah cosine of x.

[00:05:40]Interesting.

[00:05:42]So what's going on is u is equal to this product rule here. Here we could test this product rule, right? Let's test it. du the derivative of this is cotangent of x uh oh wait a minute what we get cosine of x oh oh no I miss I missed uh I miscalculated in my head no it is cosine it's cosine I was like cosine square over s the sign is already taken by co-angent x so yeah this is correct okay awesome so then this is equal to e to the 2 u du and then this is like what plug in zero you get what one plug in zero is negative infinity and then plug in pi / two is zero ah so now this is equal this is equal to - 12 of e^ -2 u 0 to infinity this is going to equal to 12.

[00:06:55]So the answer to this is 1/2.

[00:06:58]Is that what I got? Is that what they got?

[00:07:04]Yeah. Yeah. Know I just just keep it simple. Just keep it simple, right? Just factor it out. If you need to turn it into a loophole log and then realize that Oh, well experiment with with derivatives. Experiment with derivatives. And we found out that this is the correct product rule. All right, last one. I'm assuming quotients. Ah, toy easy. Toy easy. Y'all should know this. Actually, I can't do this in my head. This is to easy to Oh, it should be negative. Don't forget that. Um, be very careful. And then one to infinity, right? Infinity is zero.

[00:07:48]And then plug in one. and we get one over e.

[00:07:53]So is it one over e?

[00:07:57]You also could just invert. Yeah, one over e. Nice.

[00:08:02]Awesome. And I believe the next one is finals.

[00:08:08]Yep. Finals. Awesome. The rest is just tiebreers that we've already done by accident. Um. Yes. Awesome. Okay. Jeez.

[00:08:18]Uh, this was actually I'm really glad you guys are nice enough to not give like bashy partial fractions. I thought it was going to be a lot bashier than I thought, but it wasn't as bad. You guys actually kept it pretty simple, right?

[00:08:33]The coefficients were very clean and nice. So, I'm really thankful for that.

[00:08:40]I took the I miscalculated my arithmetic, so I thought that's how it was going to be, but no, it was actually a lot more beautiful. So, huge prop for this. It was not as nasty as I thought.

[00:08:50]Thank Thank goodness. Uh, very nice integral here. Uh, nice third place match. This one's also really nice. I like I feel like there's like a p like like a hard easy hard I feel like, but it could just be me. Very fun integral so far. Nothing too nasty or frustrating, thank goodness. So uh yeah, very nice third place match. I think this is also perfect level as well. And then the tiebreers, of course.

[00:09:21]I will never forgive this though. This is this was cruel. Okay, so that's third place match. Uh yep, after this is going to be finals round, which is where the fun stuff, that finals round. I cannot wait to see how brutal that one's going to be. So stay tuned on that. Thank you so much for watching and I'll see y'all in the next video. See you.