@@sergeantsapient no fucking way 🤯🤯🤯🤯🤯 are you serious bro????? 🤯🤯🤯🤯 i thought Mr Beast, Jenna Ortega, and Barack Obama all teamed up to teach calculus 🤯🤯🤯🤯🤯
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.
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)@@ChicPooPo0
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).
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.
using linear substitution w can directly integrate it by letting x= 3x+1 which implies integral (3x+1)^4 dx => {(3x+1)^5}/{3*5} + C => {(3x+1)^5}/15 +C
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
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
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
U can also use reverse chain rule. Basicslly reverse chain rule can be used when you have a function multiplied by its derivative or a multiple of it. So 3x-1 differentiates into 3, which is a multiple of 1, and you can write the intergal as (1)(3x-1)^4. So then you just gotta remember when its a function MULTIPLIED by its derivative, you can write the function as y = f(x)^n+1, so in this case y = (3x - 1)^5 Then you just differentiate, so dy/dx = 5(3x-1)^4 × (3) dy/dx = 15(3x-1)^4 And then how do you get from dy/dx to the origional intergral? Multiply by 1/15. So just do that to the y. So without having to change to u, or du, or change the limits if there is any, i can just tell that its gonna be 1/15(3x-1)^5 + c (Forgot the +c nvm im cooked lmao)
theres an easier way, instead of doing all that you can just do it normally, adding 1 to the power then dividing it by the answer (4+1=5) times the number next to the x (3) and u get the exact same answer with less steps
Tip: If you have a linear function of x (a function of form ax + b ) or any other variable inside another function you can treat the inner linear function as x and proceed as normal integration, at the end divide your answer with the coefficient of x. In this case : integration of (3x-4)^4, treat 3x-4 as x and integrate, (3x-4)^5/5 and at the end divide the answer by the coefficient of x in this case 3, Hence our answer is (3x-4)^5/(3×5) = (3x-4)^5/15 + C
Love it when what I'm learning directly coincides with what I'm recommended. I have been trying to finish the integration chapter the past 2 days it's AAAAARGH
There's a short trick. You can perform the normal integration like when u do with x. It will become (3x-1)^5/5 and then divide it with the coefficient of x that is 3. And get the answer
I REMEMBER DOING THIS IN CLASS OMG I remember at my friend's 18th birthday party she was drunk and I said ELLIE 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
Instead of substituting you could have just used the simple power rule of integration and just multiply the coefficient of x this trick is really handy is solving linear ones
Let's take a critical analysis of the displayed equation, let's y = (3x - 1)^(4) using the integration approach a^(n) ≈ (1/(n+1))*a^(n + 1) via substitution, so let u = 3x - 1 || u^(4) || u' = (1/5)*u^(5) || we have to also integrate the integrable variables in u, so 3x - 1 ≈ (3/2)*x^(2) - x and multiply it by the integral of u, giving us ((3/2)*x^(2) - x)*(1/5)*u^(5), it should be noted that we have to replace the original value of u = 3x - 1 into our eqn. to get our final answer ((3/2)*x^(2) - x)*(1/5)*(3x - 1)^(5)
you can do it directly by the simplest integral formula x^n+1/n+1 because it is a linear function, just have to multiply the coefficient of x at the denominator. do no forget to add C at the end.
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 💪🏻💪🏻💪🏻
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.
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.
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 can do this with anything of the form f(ax+b), basically the 'mini function' should be a linear polynomial to do this. This is used so often i most of the times don't even show the substitution and jump to the ans. Simply integrate f normally (considering the linear polynomial as ur variable) then just divide the thing by a (coefficient of x). And ofc, don't forget the +c
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."
Goofy aah this ain't 5th grade. The reverse chain rule is u-substitution but in your head. You might be able to do it fine for easy functions like these, but when the functions become more complicated, and you don't understand the actual method that you're doing in your head, you're gonna be screwed.
@@totallynotpaul6211 i do understand the method and imma keep doing it in my head, you dont know what you're yapping about 5th grade, i dont need a formula for a simple integration technique when theres a logical way of thinking about it
"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
Amen. Im sick of people bragging about IA taking jobs or thinking IA will lead to some sci-fi robot dystopia.
I love the idea of an actress, a former president, and a RUclipsr teaming up to make a calculus video.
that's how you attract common people to learn these cool stuffs
Pretty sure this is AI.
@@sergeantsapient no fucking way 🤯🤯🤯🤯🤯 are you serious bro????? 🤯🤯🤯🤯 i thought Mr Beast, Jenna Ortega, and Barack Obama all teamed up to teach calculus 🤯🤯🤯🤯🤯
@@goosemchonk pretty sure you're AI.
@@sergeantsapient pretty sure your mom's AI. she kept talking about using glue in pizza while i was clapping her cheeks
"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
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)@@ChicPooPo0
@@ChicPooPo0 I can kinda understand understand some parts as a 7th grader.
@@shadowmilkcookie6969oh I understand everything as a 7th grader 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
"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
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
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 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
i was learning integral yesterday and didnt know a single thing until this vid pls do more this help my rotted brain so much
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
BRO PLEASE KEEP MAKING THIS. THIS IS FIRE 🔥🔥🔥🔥
Revised the entire Integration in a minute. I'm subscribing immediately bro
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.
Why to even remember the Pascal's triangle when nCr is there to help you
@@MokshitArora. fr
using linear substitution w can directly integrate it by letting x= 3x+1
which implies
integral (3x+1)^4 dx => {(3x+1)^5}/{3*5} + C
=> {(3x+1)^5}/15 +C
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
Feel like you could just get the same result without AI but okay
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
This was genuinely useful, nice for revision
Calculus isn’t very hard (at least 1 2 and 3) but it takes people some time to process these things for the first time
and once again this channel has taught me more about calc than the entire time I have been in the class lol
If Jenna was my teacher i would go to school even during holidays
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! 😊
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
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
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
Keep posting more like this bro
You deserve a sub and you are gonna get it
U can also use reverse chain rule. Basicslly reverse chain rule can be used when you have a function multiplied by its derivative or a multiple of it. So 3x-1 differentiates into 3, which is a multiple of 1, and you can write the intergal as (1)(3x-1)^4.
So then you just gotta remember when its a function MULTIPLIED by its derivative, you can write the function as y = f(x)^n+1, so in this case y = (3x - 1)^5
Then you just differentiate, so
dy/dx = 5(3x-1)^4 × (3)
dy/dx = 15(3x-1)^4
And then how do you get from dy/dx to the origional intergral? Multiply by 1/15. So just do that to the y.
So without having to change to u, or du, or change the limits if there is any, i can just tell that its gonna be 1/15(3x-1)^5 + c
(Forgot the +c nvm im cooked lmao)
Reverse chain rule is just a special case of u sub where du is a constant multiple of dx
on a real note this teaches me better than my actual teacher, tysm for these
theres an easier way, instead of doing all that you can just do it normally, adding 1 to the power then dividing it by the answer (4+1=5) times the number next to the x (3) and u get the exact same answer with less steps
Thank god you put that c there, I was getting anxious about it😅
These are really helpful bro thx for ur videos
Keep up the great work, buddy🎉
Why was this so much easier to understand than any calc class
Tip: If you have a linear function of x (a function of form ax + b ) or any other variable inside another function you can treat the inner linear function as x and proceed as normal integration, at the end divide your answer with the coefficient of x.
In this case : integration of (3x-4)^4, treat 3x-4 as x and integrate, (3x-4)^5/5 and at the end divide the answer by the coefficient of x in this case 3,
Hence our answer is (3x-4)^5/(3×5)
= (3x-4)^5/15 + C
Bro this is pure perfectionist. Love it😂♥️
This is so goood
Keep making these please
This is honestly so good, it was rly good
Love it when what I'm learning directly coincides with what I'm recommended. I have been trying to finish the integration chapter the past 2 days it's AAAAARGH
i learnt about this in school a while ago and it's so wholesome that i came across this video lol
that was good. My suggestion is to make the voice sound like its recorded live like in a big room and itll be perfect.
I will try that thanks sm for the suggestion bro
There's a short trick. You can perform the normal integration like when u do with x. It will become (3x-1)^5/5 and then divide it with the coefficient of x that is 3. And get the answer
This retains my attention so well. I actually want to focus naturally
No fucking shot this was actually useful and just helped me a lot.
I REMEMBER DOING THIS IN CLASS OMG
I remember at my friend's 18th birthday party she was drunk and I said ELLIE 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
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
Instead of substituting you could have just used the simple power rule of integration and just multiply the coefficient of x this trick is really handy is solving linear ones
where was this when i needed it years ago
Thats U substitution was hell when i learning Anti derivative i remember
But this helped me alot in programing
Let's take a critical analysis of the displayed equation, let's y = (3x - 1)^(4) using the integration approach a^(n) ≈ (1/(n+1))*a^(n + 1) via substitution, so let u = 3x - 1 || u^(4) || u' = (1/5)*u^(5) || we have to also integrate the integrable variables in u, so 3x - 1 ≈ (3/2)*x^(2) - x and multiply it by the integral of u, giving us ((3/2)*x^(2) - x)*(1/5)*u^(5), it should be noted that we have to replace the original value of u = 3x - 1 into our eqn. to get our final answer ((3/2)*x^(2) - x)*(1/5)*(3x - 1)^(5)
Learning maths from Jenna Ortega, Obama , mrbeast at same time is real flex 💪
It is amazing and scary how realistic this is!
Awesome!
im gonna be starting integration in some time so this really was helpful! Kept me engaged and i even learnt something! Thanks a lot!
The graphics of the equation updating were way better than most tutorials, dang.
Thanks jenna, i am taking my PERT soon, im sure this will help
man your videos are the best
you can do it directly by the simplest integral formula x^n+1/n+1 because it is a linear function, just have to multiply the coefficient of x at the denominator.
do no forget to add C at the end.
Can you make Einstein teach me?
Wtf how am i learning math from shorts and actually remembering this.
This is how AI should be used
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 💪🏻💪🏻💪🏻
I find it easier to take out the fraction in front then you can multiply at the end. Just another option
Man ,i pray good fortunes for u creator of the vedio
this was way better than i expected it to be
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.
Came here to say just this , derivatives are actually limits , it doesn't make sense when you take the denominator out .
This new type of content is absolutely W
Absolutely insane, I want more of this
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 💯
You can take the 1/3 out the front and multiply by the integral
If there's series of this, i wouldn't be bored of math
Can you please also explain chain rule in differentiation like this, I keep getting questions based on it wrong many times
Bro ive got a vid on chain rule! Its the one with ice spice
@@onlocklearning thanksss searching it right now. I didn't know you had made it already😁😁😁
This is where calculus starts from "slightly ridicolous" to "making stuff up"
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 😭😭🙏🙏🙏
That "C" always started my villain arc
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
I thought this was gonna be some weird new marketing tactic
Never mix calculus with alcohol. Don’t drink and derive.
Thats a smart use of AI to let anyone understand this equation .
Man I used to do Fourier transforms in uni... I don't remember jack sh!t anymore 😂
This helped me more than my calculus professor
This is actually a really good way of learning.
Do this bro.its just so easy to understand
You can do this with anything of the form f(ax+b), basically the 'mini function' should be a linear polynomial to do this. This is used so often i most of the times don't even show the substitution and jump to the ans. Simply integrate f normally (considering the linear polynomial as ur variable) then just divide the thing by a (coefficient of x).
And ofc, don't forget the +c
This is PHENOMENAL! Wow. What a great way to teach math!
Congratulations, you used something very powerful in a way 99% better than everyone else.
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
Amazing method❤ gonna try~
Now this is how we use ai ✨
The guy or girl whose running this channel
A message for you : *Your amazing*
this is now my go to instead of the usual Organic Chemistry guy
I never thought this could help me😭
This made more sense than my actual calculus class lol
i just do reverse chain rule which is basically this but you can do in your head and easier to think about (for me at least)
Goofy aah this ain't 5th grade. The reverse chain rule is u-substitution but in your head. You might be able to do it fine for easy functions like these, but when the functions become more complicated, and you don't understand the actual method that you're doing in your head, you're gonna be screwed.
@@totallynotpaul6211 i do understand the method and imma keep doing it in my head, you dont know what you're yapping about 5th grade, i dont need a formula for a simple integration technique when theres a logical way of thinking about it
That only works for functions where the derivative of the inside is constant tho while u sub works when it isn’t