Yeah. It's quite ez to understand for those who know integration but for those who don't, it's neither a brainrot nor a brain growth I would say(It's atleast not a brainrot bro, please do not give me an argument about this)@@lienzomoho15
Also AI: Flirts with VTubers, gaslights, trolls and roasts everyone, tells stories and has just recently learned that 10+9 equals 19. And the other A.I. just acts as if it is evil but is in fact pretty wholesome and cute. In other words, if such A.I.s would one day conquer the world, 4Chan will be the parlament while the A.I.s are the presidents.
omfg i know how to do integration chain rule cuz of some 1:28 video of jenna ortega, obama and mrbeast ai doing math on youtube. This is truly the 21st century
This video managed to teach me two things. A handy integration trick and the fear of the constant development of AI that at this moment, can now copy someone else's voice and make them speak.
There's also reverse chain rule: - Increase power, so (3x-4)⁴ becomes (3x-4)⁵ - Divide by new power, so (3x-4)⁵ becomes (3x-4)⁵/5 - Divide by derivative of inner function, so (3x-4)⁵/5 becomes (3x-4)⁵/15 Also the +c of course
@@rahulbansal2 Yeah, it looks like he just skip the step of writing the u-substitution to the side. It feels like a way of doing if you are on the lazy side, haha.
A helpful note is that the derivative of the u-substitution must already be present in the integral in some form; otherwise, you cannot perform a u-substitution and must choose another integration technique.
Wouldn't the derivative of u always be present in the integral in some form because we are choosing u? 3 isn't in the integral. 3x-1 is in the integral. (1/3) is factored out of the integral because it is a constant.
@@iMagUdspEllr Yes, the derivative must be present in the integral (since u-substitution requires the integrand to be in the form f(g(x))g’(x)), but it’s okay for the only difference to be a constant coefficient; in your example, u=g(x)=3x-1, du/3=dx basically scales the integrand from 3f(u) to f(u); otherwise, you’ve basically tripled the area in the process of substituting.
@@iMagUdspEllr The second one is correct! With the former, I would use a Pythagorean identity to write all trig functions in terms of either sin or cos, distribute, and use reduction formulas for sin^n(x) or cos^n(x).
THIS is a huge example of how the internet and AI can actually be helpful tools, if people behind it have the right intentions. Amazing. Thank you lots, I was having a lot of difficulty understanding that concept in my calculus 1 class
Much easier way to do it would be reverse chain rule but I gotta admit, I do love a good substitution for integration, definitely one of if not my favourite method
The u-substitution is basically just the explicit version of the reverse chain rule here, so I’d say they’re equivalent. (In reality, all u-substitutions are applications of the “reverse chain rule” by definition.)
@59xthepain87 yeah in most cases especially since reverse chain rule only works in specific cases but in this case reverse chain rule is much quicker and easier so there is no point in using a u substitution cause it's so much longer
I aced AP Calculus exam with a score of 5.0/5.0, and got full credit for Calculus courses in university. That has no use in real life unless you are teaching Calculus at school. Then I studied Accounting. No use whatsoever. Just adding and subtracting. Even those are tricky; otherwise, you go to prison. Accountants know what I meant by that. Calculus makes me shake my head.
Fun fact: Expanding the power of any binomial is actually extremely easy! You just need to know Pascal’s triangle. Given (a + b)^n, the coefficients of the resulting polynomial are equal to the numbers of Pascal’s triangle at the layer n+1, and the powers of a and b are, respectively, n-k+1 and k-1, where k is the horizontal position on Pascal’s triangle. It’s easier to show it with an example: Let’s take (a+b)^4, and let’s construct Pascal’s triangle’s 5th level: 1 1, 1 1, 2, 1 1, 3, 3, 1 1, 4, 6, 4, 1 Now, we know that the resulting polynomial will be ab + 4ab + 6ab + 4ab + ab. Now, let’s add the powers to a and b: (a^4)(b^0) + 4(a^3)(b^1) + 6(a^2)(b^2) + 4(a^1)(b^3) + (a^0)(b^4) If the original polynomial was (a-b)^n, every other component is negative. (a-b)^4 would be: (a^4)(b^0) - 4(a^3)(b^1) + 6(a^2)(b^2) - 4(a^1)(b^3) + (a^0)(b^4) It looks complex, but once you’re in front of an exercise it saves a lot of time, and you can easily do it in your mind if you know the rules.
2019: "AI will take over the world!!!" 2039: "Learn US history by playing an AI-generated VR game recreation of famous events like the Boston Tea Party and Civil War narrated by the president of the time."
I REMEMBER DOING THIS IN CLASS OMG I remember at my friend's 18th birthday party she was drunk and I said WLLUE YOU'RE PROBABLY SO DRUNK YOU CAN'T EVEN INTEGRATE and she said YEAH I CAN and I gave her an integral and SHE FUCKING VERBALLY BANGED IT OUT ON THE SPOT IT WAS AMAZING
Surely Jenna Ortega is a real human being. She doesn't always have the answers. Everyone can Google it and feel inspired to come up with answers of their own.
Mehhh its not believable, they are US people, its imposible to imagine someone from the usa saying inteligent things, and even less imagine them beeing smart at all.
We don’t even have to substitute actually , since 3x-1 is a linear function , we can straightaway integrate it using inverse power rule and divide it by 3
0:49 A point to note that you cannot rearrange dx simply like division, to RHS since d/dx itself is a function...you should use differential instead of Differentiation...that would help you all not making small mistakes in calc class
The technique of heuristically treating (d/dx)u (the derivative operator applied to u) as a ratio of two infinitesimals is more or less the entry-level approach to the differential forms you’re talking about, but yes, it also helps to know why “multiplying both sides by dx” works by understanding what differentials are.
As a brainrot victim and scrolling addiction, I can confirm that this rare ai short form content is actually educational and very informative that it doesn't "rot" my brain but rather make it stronger 💪🏻💪🏻💪🏻
No joke, I'm 26 and sometimes I still have nightmares about having to do math tests in school and feeling like shit. What a relief that this is over for me
Can u pls do this with US presidents? (Trump, Joe and Obama)? Also The Rock! Also u can do like programming and reverse engineering stuff it would be so cool! I really loved the US presidents play "Escape the Backrooms" series. Pls do with US presidents I bet everyone would love it!!
I'd suggest as a cosmology enthusiast that this TH-camr he's uploading theses TH-cam videos form another parallel universe where people actually like maths and that's why all these big guys are talking about maths 😂😂😂
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him. John 3:16-17 Jesus loves you 🔥🔥🔥 pls don't take this the wrong way
Great, that is the method used, but they did not explain why the substitution can be done. And it can be done because u:x |----> 3x-1 is continuous and differentiable and its derivative is continuous everywhere, for all real number x.
Why wouldn’t you just simplify the powers? Or use the power rule to further simplify The function? Learning calc rn so lmk why it’s this way and not another
"How are you so good at calculus??"
"Obama"
Jimbo
Thanks Obama!
Thanks Obama :D
Obombna
Thanks Obama
A rare example of AI not being used for shitpost nor nefarious content
But nefarious content is the most fun
@@SidPil Exactly, I use it to make spicy images of girls
But this is still a form of shitpost. Like Integrating with Chud
@@braziliantsarweirdly enough i actually understand u sub better now bc of a shitpost
@@algirdasltu1389now is it really a shitpost? Its more of a usefulpost
I love the idea of an actress, a former president, and a TH-camr teaming up to make a calculus video.
that's how you attract common people to learn these cool stuffs
brainrot ❌ brain growth ✅
🔥
If you could understand that hoolabaloo
Yeah. It's quite ez to understand for those who know integration but for those who don't, it's neither a brainrot nor a brain growth I would say(It's atleast not a brainrot bro, please do not give me an argument about this)@@lienzomoho15
@@lienzomoho15 I can kinda understand understand some parts as a 7th grader.
@@shadowmilkcookie6969oh I understand everything as a 7th grader lol
"AI will take over the world"
AI: "How to integrate using U substitution"
Lol its better than the brain rot content kids use it for
@@ishaanverma5765Fr
Also AI: Flirts with VTubers, gaslights, trolls and roasts everyone, tells stories and has just recently learned that 10+9 equals 19.
And the other A.I. just acts as if it is evil but is in fact pretty wholesome and cute.
In other words, if such A.I.s would one day conquer the world, 4Chan will be the parlament while the A.I.s are the presidents.
Well all AI is really doing here is imitating the voices I think
@@edgelord383 no shit Sherlock
brain nourishment
brain blooms and flourishes
Until it's Ordinary diff equations or just definite integrals in general
@@Ichigo-gp9vqlinear ode are very nice
@@Ichigo-gp9vqwhat's the problem with definite integrals?
@@leocherry They make me wanna reconnect with nature
"Thanks Jimbo" 😂
That part got me too😂
"Looks like you're going to the shadow realm, Jimbo"
I nearly fell off my chair after that one lol
omfg i know how to do integration chain rule cuz of some 1:28 video of jenna ortega, obama and mrbeast ai doing math on youtube. This is truly the 21st century
Celebrities becoming math ed influences was not on my AI bingo card
Obamna 🥺
SODA!!!1!!!🥤🥤🥤❗️❗️‼️‼️⚠️⚠️🗣️🗣️🗣️📣📢📢📢🔊🔊
SODA!!!🗣🗣🗣
SODAAAA 🗣️🗣️🗣️🗣️🗣️🗣️🔥🔥🔥🔥🔥🔥🇺🇸🇺🇸🇺🇸🦅🦅🦅🦅🦅🥤🥤🥤🥤
America is a nation that can be defined in a single word
I am atomic.
This is really helpful
Yeah this is genuinely one of the best explanations I've seen. It doesnt overstep, but teaches just enough for it to make sense
Hate how they are teaching it like they are teaching a 5th grader
@@ishaankumar4587 Maybe the Target audience wasn't you
@@ishaankumar4587bro you too smart it would seem. But for those who didn't know this before, it's really helpful
@@ishaankumar4587bro you too smart it would seem. But for those who didn't know this before, it's really helpful
This video managed to teach me two things.
A handy integration trick and the fear of the constant development of AI that at this moment, can now copy someone else's voice and make them speak.
Thankfully AI images and videos still aren't impossible to differentiate from real ones
@@hooman9554 yet💀
You forgot to add C
@@Kromiballfr
@@Thisorthat00009 fr 💀
"don't be a goofy goo and add the c" had me laughing so hard 🤣
There's also reverse chain rule:
- Increase power, so (3x-4)⁴ becomes (3x-4)⁵
- Divide by new power, so (3x-4)⁵ becomes (3x-4)⁵/5
- Divide by derivative of inner function, so (3x-4)⁵/5 becomes (3x-4)⁵/15
Also the +c of course
Oh I haven't learned the reverse yet this seems much easier
@@rahulbansal2 Yeah, it looks like he just skip the step of writing the u-substitution to the side. It feels like a way of doing if you are on the lazy side, haha.
This is what I do (I’m lazy)
It is known as basic manipulation in our culture
I was gonna comment this but did it first.
A helpful note is that the derivative of the u-substitution must already be present in the integral in some form; otherwise, you cannot perform a u-substitution and must choose another integration technique.
Wouldn't the derivative of u always be present in the integral in some form because we are choosing u? 3 isn't in the integral. 3x-1 is in the integral. (1/3) is factored out of the integral because it is a constant.
@@iMagUdspEllr Yes, the derivative must be present in the integral (since u-substitution requires the integrand to be in the form f(g(x))g’(x)), but it’s okay for the only difference to be a constant coefficient; in your example, u=g(x)=3x-1, du/3=dx basically scales the integrand from 3f(u) to f(u); otherwise, you’ve basically tripled the area in the process of substituting.
@@matchamitminze So cos(x)^2*sin(x)^2 doesn't work, but cos(x)*sin(x)^2 works? (If u=sin(x)?)
@@iMagUdspEllr The second one is correct! With the former, I would use a Pythagorean identity to write all trig functions in terms of either sin or cos, distribute, and use reduction formulas for sin^n(x) or cos^n(x).
@@matchamitminze I see. Thank you!
When i was a kid i couldnt even imagine that all the celebrities would be able to teach kids in schools in future
There was no need for U substitution in this question💀
This is so goood
THIS is a huge example of how the internet and AI can actually be helpful tools, if people behind it have the right intentions. Amazing. Thank you lots, I was having a lot of difficulty understanding that concept in my calculus 1 class
This taught me more than any math class I’ve taken
Means you know no math
Maybe you need to actually start listening to the teacher☠️
bro graduated from mcdonalds icecream machine
Probably sleep through the whole class
Stop, they're already dead
This is how AI should be used
Can you make Einstein teach me?
Much easier way to do it would be reverse chain rule but I gotta admit, I do love a good substitution for integration, definitely one of if not my favourite method
The u-substitution is basically just the explicit version of the reverse chain rule here, so I’d say they’re equivalent.
(In reality, all u-substitutions are applications of the “reverse chain rule” by definition.)
i promise you just using a u sub in general is much better than reverse chain rule.
@@59xthepain87 People applying the “reverse chain rule” are just doing a mental u-substitution, so they’re not really different things.
@matchamitminze yeah I know but reverse chain rule is so much quicker
@59xthepain87 yeah in most cases especially since reverse chain rule only works in specific cases but in this case reverse chain rule is much quicker and easier so there is no point in using a u substitution cause it's so much longer
0:46 my calc teacher taught us to write that as 1/3 times du so that we can just take the 1/3 constant out of the integral
Same
That can be even more helpful on definite integrals imo
But how would that help you... it's a 'trick' that only helps you when you still have trouble with simple integration
@@MrTrollo2it’s not a matter of how hard it is, it just declutters the integral itself. Especially if you’re taking a definite integral.
You can take it out the integral or you can keep it in it doesn’t matter either way so just do whichever you’re more comfortable with
Revised the entire Integration in a minute. I'm subscribing immediately bro
Now this is how we use ai ✨
The guy or girl whose running this channel
A message for you : *Your amazing*
I aced AP Calculus exam with a score of 5.0/5.0, and got full credit for Calculus courses in university. That has no use in real life unless you are teaching Calculus at school. Then I studied Accounting. No use whatsoever. Just adding and subtracting. Even those are tricky; otherwise, you go to prison. Accountants know what I meant by that. Calculus makes me shake my head.
Fun fact:
Expanding the power of any binomial is actually extremely easy! You just need to know Pascal’s triangle. Given (a + b)^n, the coefficients of the resulting polynomial are equal to the numbers of Pascal’s triangle at the layer n+1, and the powers of a and b are, respectively, n-k+1 and k-1, where k is the horizontal position on Pascal’s triangle.
It’s easier to show it with an example:
Let’s take (a+b)^4, and let’s construct Pascal’s triangle’s 5th level:
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4, 1
Now, we know that the resulting polynomial will be ab + 4ab + 6ab + 4ab + ab. Now, let’s add the powers to a and b:
(a^4)(b^0) + 4(a^3)(b^1) + 6(a^2)(b^2) + 4(a^1)(b^3) + (a^0)(b^4)
If the original polynomial was (a-b)^n, every other component is negative. (a-b)^4 would be:
(a^4)(b^0) - 4(a^3)(b^1) + 6(a^2)(b^2) - 4(a^1)(b^3) + (a^0)(b^4)
It looks complex, but once you’re in front of an exercise it saves a lot of time, and you can easily do it in your mind if you know the rules.
2019: "AI will take over the world!!!"
2039: "Learn US history by playing an AI-generated VR game recreation of famous events like the Boston Tea Party and Civil War narrated by the president of the time."
lowkey this idea is fire, feel free to implement this in classrooms @USAgovernment just credit me in the end screen
i was learning integral yesterday and didnt know a single thing until this vid pls do more this help my rotted brain so much
I REMEMBER DOING THIS IN CLASS OMG
I remember at my friend's 18th birthday party she was drunk and I said WLLUE YOU'RE PROBABLY SO DRUNK YOU CAN'T EVEN INTEGRATE and she said YEAH I CAN and I gave her an integral and SHE FUCKING VERBALLY BANGED IT OUT ON THE SPOT IT WAS AMAZING
on a real note this teaches me better than my actual teacher, tysm for these
Another way to do this is to divide by the "a" term in a (ax+b)^n
You can skip the whole du/dx with this
reverse chain rul
There's a direct formula to do (ax+b)n model problems 😂 (ax+b)n+1/a*(n+1)
all that for, one drop of blood ? *Tells in Thanos voice
The fact that my school math proffesor looks very similar to Jana Prtega does not help a single but lmao
0:20 What was the name of the bg music?
TheFatRat - Xenogenesis
@@Afire50M I knew it was fatrat's song, but I didn't know the name. Thanks.
I hate this u substitution cuz i learned it with t
Truly a braingrowth video
3/5 (3x-1) to the fifth + c boom all in my head in under a minute
I’m a dumbass its 1/15 (3x-1)^5 +c
Bro this is such a basic integration in class 12 india
Jenna Ortega solving❌AI solving✅
Using AI I can learn math from anyone including my favourite celebrity, my parents even my little sister will be my math teacher.😂
In my eyes, their mouth movements weren’t matching what I was hearing them say.
Must have been extremely edited, or I just really need my glasses.
It tooks me half of a video to realize that this is AI.
Is it?
Thats a smart use of AI to let anyone understand this equation .
Learning maths from Jenna Ortega, Obama , mrbeast at same time is real flex 💪
Why was this so much easier to understand than any calc class
BRO PLEASE KEEP MAKING THIS. THIS IS FIRE 🔥🔥🔥🔥
Bro we have calculus finals tomorrow and this might work 😭😭
good luck bro you got this 🔥
@@onlocklearning thank you😭🙏🙏🙏 I appreciate your comment and the brain nourishment video 😭😭🙏🙏🙏
Thank god for this recommendation, I got my Calc exam in 2 days and completely forgot about this
That means you don't know very much, fam. How'd it go, ya failed?
@@CeRz It happened
@@duckyfam9012 next time! Good luck! 😊
Keep posting more like this bro
I don't understand this, I barely know what a function is.
Oh please please do Hughie Laurie as HouseMD
Bro this is pure perfectionist. Love it😂♥️
This is a genius use case for AI! Congratulations!
Mr Beast joining in caught me off guard 😅
Surely Jenna Ortega is a real human being. She doesn't always have the answers. Everyone can Google it and feel inspired to come up with answers of their own.
Exactly 💯
It took me 0.1sec to answer
Yes I'm jee student
Congratulations, you used something very powerful in a way 99% better than everyone else.
Mehhh its not believable, they are US people, its imposible to imagine someone from the usa saying inteligent things, and even less imagine them beeing smart at all.
lol
I just use Matlab symbolic solver…
If jenna teaches I'll get 10 PhDs 😂😂
Brain Growth 👍 ✅
Simple answer Integrate/differentiate
We don’t even have to substitute actually , since 3x-1 is a linear function , we can straightaway integrate it using inverse power rule and divide it by 3
Now this could be taught in school!
This mf is better than any teacher i ever had
Actors aren't acting their IQ
W
I FORGOT TO ADD THE C AGAIN FUUUU!
0:49 A point to note that you cannot rearrange dx simply like division, to RHS since d/dx itself is a function...you should use differential instead of Differentiation...that would help you all not making small mistakes in calc class
The technique of heuristically treating (d/dx)u (the derivative operator applied to u) as a ratio of two infinitesimals is more or less the entry-level approach to the differential forms you’re talking about, but yes, it also helps to know why “multiplying both sides by dx” works by understanding what differentials are.
aur log deko
highly recommndid
You deserve a sub and you are gonna get it
This is kinda terrifying.
Wednesday how th you learned calculus?! MAN I THOUGHT I ESCAPED THE WEDNESDAY DANCE TREND
You forgot to add the Constant C
Calculus is just amazing.
Obama❌ The Rock✅✅😂
As a brainrot victim and scrolling addiction, I can confirm that this rare ai short form content is actually educational and very informative that it doesn't "rot" my brain but rather make it stronger 💪🏻💪🏻💪🏻
Меня успокаивает это видео
This was genuinely useful, nice for revision
Her lips is giving out😂
HAHA this is scary how many views you got with this video! I'll be watching you!
This just taught me that I definitely don’t remember any of the calculus I learned 20 years ago
We use 'z' instead of 'u'
I wish these were real :(
i learnt about this in school a while ago and it's so wholesome that i came across this video lol
No joke, I'm 26 and sometimes I still have nightmares about having to do math tests in school and feeling like shit. What a relief that this is over for me
You'd better this formula which we use in Poland:
If: ſf(x)dx = F(x) + C
it means that:
ſf(ax+b)dx = 1/a F(ax + b) + C
d/dx = 1/x
Can u pls do this with US presidents? (Trump, Joe and Obama)? Also The Rock! Also u can do like programming and reverse engineering stuff it would be so cool! I really loved the US presidents play "Escape the Backrooms" series. Pls do with US presidents I bet everyone would love it!!
Thanks jenna, i am taking my PERT soon, im sure this will help
Thanks! I always wrongly put the 1/3 out of the integration... thanks for the illustartion. I know the skill but remember the rule wrong!
I'd suggest as a cosmology enthusiast that this TH-camr he's uploading theses TH-cam videos form another parallel universe where people actually like maths and that's why all these big guys are talking about maths 😂😂😂
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him.
John 3:16-17
Jesus loves you 🔥🔥🔥
pls don't take this the wrong way
= (3x-1)^5/15+ C
ai getting damgerous
making "dx" the subject is mathematically, or rather conceptually incorrect btw, since du/dx means the derivative of u with respect to x
Great, that is the method used, but they did not explain why the substitution can be done. And it can be done because u:x |----> 3x-1 is continuous and differentiable and its derivative is continuous everywhere, for all real number x.
After watching this tortorous video ,My brain has rised the maximum boiling point,infact I don't have some sort of cooling mechanism...
Why wouldn’t you just simplify the powers? Or use the power rule to further simplify The function? Learning calc rn so lmk why it’s this way and not another