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
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
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
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.
it's amazing to understand.
Love from INDIA 🇮🇳
A little mistake in the answer. It is ln[(2+√7)/√3], in the second term. Kindly re-check it.
積サーからきた
ingenious
how did you know to express such a nested radicalled polynomial as the sum of two radicals?
Thanks for this interesting video. Note that at the time:5:55 the sin^2u should be sinh^2u.
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
I’ve been seeing the word “esoteric” used a lot recently. noice
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
Maths505 But your solution is also nice
It eas really awesome. Respect from Bangladesh 🇧🇩
THAT ANSWER WAS SUPPOSED TO BE A SQUARE ROOT OF 3 UNDER THE 2+ SQUARE ROOT OF 7
im kind of confused as to how we went from x+1/2 to sqrt(3)/2*sinh(u)
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.
Who?
@@Walczyk The finalists from MIT integration bee
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
Dude Just use a computer algebra system
Did you type this comment in the 1800s lol
@@maalikserebryakov i managed to solve it eventually
would you like me to type unrendered tex instead
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
Sorry mate it's just something i struggle to say correctly
I would use tan instead of sinh since i understand its inverse a bit better.
Sinh is better in most cases as it is cyclically differentiable and more fundamental
この動画を見に来る変態日本人は僕だけか
よぉ
I'm late to the party! no! glorious solution my comrade ;)
(a-b)^2 = x^2 is |a-b| = x. Doesn't it?
Yes. Maybe x = b - a is spurious? I haven't done the algebra.
聖地巡礼
coolio
VERY difficult to read. Use BRIGHTER colors and thicker lines.
What a PhD did to blud’s eyes