the hardest integral from the BMT integration bee
The Fall 2023 Berkeley Math Tournament will be held on the UC Berkeley campus on Saturday, Nov. 4th and I will be there! For more info and registration, check out berkeley.mt/events/bmt-2023/.
I solved this monster improper integral during the Extreme Calculus Calculus (another 100 integrals). Full video • 100 integrals (almost ...
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The Fall 2023 Berkeley Math Tournament will be held on the UC Berkeley campus on Saturday, Nov. 4th and I will be there! For more info and registration, check out berkeley.mt/events/bmt-2023/.
I’m laughing when he said “I know this has the N but that’s ln” his facial expression and the way he delivered is killing me😂.
Same
Lol😂
HAHAA SAMEE
😂
Ya, and what makes it extra funny to me is that these types of jokes he makes might have come from IRL mistakes he saw at some point :D
This is why I love this channel. Takes an integral that, quite frankly, almost makes me wanna cry, and turns it into something where I just need to brush up on infinite series to understand.
Looks so complex yet it’s so simple! Thanks for the tutorial, you never disappoint. 😊
Thanks!
@@blackpenredpen No problem! Also I wanted to point out that I’ve been watching you for a while now and never expected you to see any of my comments, let alone reply to one! Thanks so much for replying, it made my day ❤️
That was fun. Thanks. I thought it was interesting that the integral itself wasn't that hard, but rather the simplification of the series. Have you ever thought about getting refillable pens? They work great.
One of most unique integrals I’ve seen in a while
🤣🤣7:49.... He has done his work & there's no reward except this mad behavior.
I wouldn't have been able to do this on my own, but man is this one satisfying
7:50 "And that's a good place to stop."
I love your videos. Over the years you’ve always been so helpful, so direct, and so charismatic. Even if I don’t understand what’s happening it’s still entertaining. Thank you
Thank you!
That was fun! I have not done calculus classes since 1980 as a mathematics major but I could follow this! Great work and explanations!
Feels great to be able to solve it while being in high school. Thanks bprp. You started my year old obsession with integrals🙇♂️.
EXCELLENT VIDEO, thank you for this. I struggled so much with infinite series, it's nice to see a fairly practical application of it to solve an incredibly difficult problem
I did this integral after 100 integrals lol full video kzhead.info/sun/nbWzYcuJaWaFe5s/bejne.html
1,000,000 SUBS
Hi.
I passed the hardest topics in Calculus thanks to you. Love how detailed your videos are.
This is just beautiful!!! Love your work!!
My first instinct was "this probably simplifies to some kind of summation involving e," but I have no clue how to get there, lol.
THAT WAS AWESOME! thanks bprp :)
It's so simplistic and beautiful, what an awesome integral
On a side note, we would be screwed if we didn't have Euler's symbol
Very fun integral, adding it to the list!
Crazy how I know all the tools he used and still I coudn't solved it myself.
And even better, e - 1/e is W^-1(1) + W^-1(-1) W(x) is the lambert W function
2sinh(1) is even better imo
@@aadhavan7127 😂😂😂
Not doing maths anymore but it is a sheer joy to watch you doing all these interesting problems
Same here. His joy is relatable, for 20-year old me.
Bro didn't know how to solve the integration He is the integration
this is a beautiful one , like after seeing how its done it dosen't seem hard but it would probably take me days before actually seeing the Maclaurin Series for e^x with the ln x being there, props to the guys that found this beauty
This is incredible solution 👍
Perfect as always 👏👏
It is probabbly the most beautiful integral I've ever seen.
Amazing mathmatical thought！using known theory to present unknown situation,for example we have learned the sum of x divided by n! is e to the power of x,then lnx is e to the power of lnx which means x,that simplified this question a lot! I 've learned a lot via watching your video!
That was a beautiful solution,clever
I am currently learning series and sequences in high school and this was so cool to see!
you have series and sequences in Highschool curriculum? Isn’t it college level?
@@kpax9284 its taught in AP bc calc, taught in high school
@@kpax9284 Pre-calc junior year most likely.
Amazing video! So much fun to watch!
This is glorious!
Gotta love when things cancel out and you get a neat and manageable solution.
Amazing !
Really Integration Bee very interesting. Thanks for video. For MIT integration bee recently it was published a book with solutions to problems of Qualifying Tests from 2010 to 2023
You are the best! 🔥🔥🔥
I'm a math tutor at my college, I gotta practice that two pen technique! I love using different colors when I'm helping students.
This was a fun one!
Thats such a cool question
This is such an easy solution when you see someone else do it, but I would have never solved it by myself!
Let y = f(x), where f(x) is the integrand. Then after some tedious manipulation one has ln y =-1 + e^(ln x) = -1+ x So y = e^(x-1) The integration can be simplified as Integrate[e^t, {t, -1, 1}] = e^t, {t, -1, 1} = e - e^(-1) Hence, Integrate[f(x), {x, 0, 2}] = e - 1/e.
I was missing your videos. =)
Sir I m ur die hard fan Really amazing content delivered
So good! 😁
pretty easy ngl did it as soon as i thought of writing the radicals in terms of powers and the x^a must been some series expansion :)
To the folks who want a more compact form: 2sinh(1). The hyperbolic sin function.
Good job sir black 👍
You could also use expansion of taylor series of e^x (its n-th derivative is always e^x) so that sum of those powers of x equals (x-1)/lnx and then substitute it back into the integral. Thats how i got it. Sorry for my english.
I solved it without watching the video! I feel so proud!
I Didn't expect to solve this myself in 5min lol
What a beatiful integral and mathematics!
You deserve 500m subscribers
Oh great question, not that difficult btw. I thought it would require some sort of wizardry, but when I wrote the question and simplified to the power of x, I quickly saw e^ln x, just needed to multiply and divide by ln x and create the e^x series, then it was pretty simple :) Once again, a great and simple question which emphasizes on finding patterns
I used to be able to solve questions of this difficulty level 10 years ago. I forgot most of the things and only remember some basic integral and derivatives formulas and concepts now :P Anyway this was cool to watch :)
The way he speaks softly and calmly, and is reassuring, reminds me of Steve from Blues Clues, except with integrals. :B
Integrating like a boss.
Goddamn was that a beauty of an equation
Your are the best bro 👍
You too
Hello Professor. I applied to UC Berkeley this year so I might see you on campus next year if I get in. If I do I’ll definitely join the Berkeley math tournament.
I don’t teach at UC Berkeley. I live in the SoCal area but I go back to UCB campus whenever I can 😃
@@blackpenredpen Oh. Where do you teach then?
@@rhversity5965 he teaches in kenya
Love even the Klein bottle behind you!
Your are great sir ❤❤😊
Amazing, that was amazing
Sir math is love for you and me❤️
The braingasm at the end
One of the best integrals I've ever seen. :)
It means you have not even seen 1% of the integral problems...
Calculus is so fascinating
At first when i saw the thumbnail, i was like wtf is this. Then i saw him sythesize its complexity. It made it easier to solve in my head. Good ol' Calc II
Loved it
I love your content man. Now that I’ve solved it it seems almost trivial - of course it’s just an infinite series, :p
Fun. watching these videos make you learn methods to solve problems.
Very interesting and not so difficult to solve if you know series. Honestly I haven’t expected to solve that without substitution or partial integration
Beautiful! So easy to follow along with your argument. But, to come up with it on my own? Sheesh, it would take me months, maybe infinite months!
Diretamente do Brasil
Integrals like this are rarely hard. They are just time consuming because they require a bit of algebra. Once you simplify the integrand by knowing a power series, there are no integration techniques required. This problem is more like a race than a puzzle. But that's what most bee integrals are. You can't put many genuinely difficult integrals in an integral bee because of the format.
Take my 👍. Great job
Mom! A new bprp is here!
In √-1 put e^iπ and take out the root of -1
7:50 when u forget u r mathematician not martial artist.
He is a jewel
HES POPPUNG OFF
I needed a u substitution, e^u=x. To see the pattern, but when I got to e^(e^u+u-1)du, I converted back to the x world.
amazingly good
Brilliant
I didn’t understand any of that but it was entertaining
the laugh at the end...
so elegant 😍
did this one in my head
this dude can quick-select between a red and blue whiteboard marker
Before the Solution : Integral is easier but that series to be formed is main thing which is like (2^n)/(n^2)
Please do the derivation of ln(-1)
I solved this after substituting x=e^t but the fact that you didn't even need to substitute jackshit is too gawddamn impressive🔥🔥🔥🔥
Making of the thumbnail........this guy....give me that fucking medal 🏅
I did this on my own just messed up a lil in the last . yay
beautiful
Mathematics is the beginning of opening the mind and knowledge of the world and the universe ❤️❤️❤️
This was an easy problem, (no offense), but the first thought in my mind was trying through u-substitution but I guess it would be easier to use Taylor series for defining e I mean it was pretty tough for some speed solving like an integration bee, but problems like these make you know about the essence of series...
Fantástico.
First time I’ve seen x to the power of a series! Lol
Me watching this as an 8th grader and not knowing calculas; hmm interesting