A savage integral from the 2023 MIT integration bee finals (problem 3) 

Really cool evaluation and great conversion of the fearsome looking nested radical into a sum of two benign radicals. This channel is getting more and more awesome by the day. I would love to have you do all the steps, your evaluation techniques are great and it would do a world of good for serious lovers of calculus, like yours sincerely.

It's really cool i got to know a new technique to integrate the function of this type, i was trying to take x^2 common from the function inside the second root but i got stuck because i thought i will get the square out from but i got extra term I can't integrate thanks to you now i know how to integrate these kind of questions.

Sire, I want to know how much of a positive impact you’re having on this community. It’s not easy to make videos on math and it’s especially difficult to make videos on math that even the most ardent math fans will find hard. That’s what I find especially inspiring about you, you manage to do math like it’s an esoteric craft with its own culture and everything. At least that’s what’s I feel when watching your videos, I don’t feel like I’m watching a math video but a gaming video because you approach it with that same level of passion. I hope you continue to make awesome videos like this. Thank you for this treasure trove of a channel :D

Thanks for this interesting video. Note that at the time:5:55 the sin^2u should be sinh^2u.

I was surprised they didn't manage to do it in the finals, as it seems much easier than problem 5, which they actually did.

Firstly observe that we integrate even function on interval symmetric around zero but even without this it is quite easy to integrate indefinite integral Euler's substitution twice and you will get rational function to integrate sqrt(x^4+x^2+1) = u - x^2 sqrt((2u+1)(u-1)) =(u-1)w for example

it's amazing to understand. Love from INDIA 🇮🇳

THAT ANSWER WAS SUPPOSED TO BE A SQUARE ROOT OF 3 UNDER THE 2+ SQUARE ROOT OF 7

A little mistake in the answer. It is ln[(2+√7)/√3], in the second term. Kindly re-check it.

It eas really awesome. Respect from Bangladesh 🇧🇩

ingenious how did you know to express such a nested radicalled polynomial as the sum of two radicals?

積サーからきた

do you do requests? i had an interesting exam question that had d^2y/dx^2 = 8/y^3 as an answer and i was wondering if you could solve the differential equation and get the original equation? the initial conditions are: when x = 1, y = 3

im kind of confused as to how we went from x+1/2 to sqrt(3)/2*sinh(u)

(a-b)^2 = x^2 is |a-b| = x. Doesn't it?

What does he mean when he says you substract the equations? it seems like some kind of subtraction or something but i dont entirely understand

I would use tan instead of sinh since i understand its inverse a bit better.

この動画を見に来る変態日本人は僕だけか

I'm late to the party! no! glorious solution my comrade ;)

VERY difficult to read. Use BRIGHTER colors and thicker lines.

唆るぜぇ゙〜これわぁ゙~

聖地巡礼

coolio