Calculus SPEEDRUN (U-Sub)!!

[@SebastianRodriguez-rk4vx]

This is a simpler problem that doesn’t require substitution, but does a good job explaining the overall concept

[@SuperStudiousman]

It took me 5 seconds to do it

[@Rizvi-2]

Took me just a flich​@@SuperStudiousman

[@Phantommm26]

It's the foil method right? Correct me if I'm wrong 😅

[@Phantommm26]

If doing foil method it's going to beX³/3 + 2x² + 4x + C... Am I right? Because I had one problem like this in my previous quiz, but we were not required yet to do u-substitutions, because we we're just getting started 😭

[@VideosViraisVirais-dc7nx]

I haven't learned it at school yet. So it's very hard to evaluate

[@wolfiegames1572]

Nah, true chads make it the integral of x^2 + 4x + 4 to get x^3/3 + 2x^2 + 4x + C

[@KewlWIS]

fact

[@m.guypirate6900]

now do that for (x+2)^20

[@saturapt3229]

@@m.guypirate6900 same stuff u gotta calculate in the end anyway

[@violintegral]

@@saturapt3229 no it isn't lol

[@gabrielfoos9393]

Just use Pascal’s triangle lmao but good luck finding the coefficients

[@jorgegarza4172]

Calculus is like a Minecraft tutorial it starts off nice, and then the problem immediately starts using 335.67 different letters

[@CosmicConvict1]

Exactly, I was like, Ok, Ok, yeah that makes sense ... WHAT THE F***

[@damontayy1272]

that's because you're focusing on how the teacher solves a problem and not focusing on the formula. When you familiarize the formula, all you have to do is substitute variables and simplify it with basic algebra. The biggest problem is if you take a calculus course without mastery in algebra.

[@jorgegarza4172]

@@damontayy1272 Calculus has so many formulas, memorizing them isn’t gonna help, you need to physically imbed the fundamental concepts into your mind to familiarize the other concepts

[@damontayy1272]

@@jorgegarza4172 I know. But guess what, you have to do hard shit to be able to amount to something. Your professor won't change the syllabus, you have to comply or shift to culinary school.

[@VIKTORSCHAUBERGERscammersONyt]

That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. @@jorgegarza4172

[@jtris01]

You don't even need u-sub. Its a linear function with coefficient of 1, so du will just equal dx.

[@leo_1304]

i think the point was for it to be an easy application of U sub. to make it easier to understand for beginners

[@jacobstarr9010]

Yeah but u sub is easier in this case

[@helphowdoinputusername3571]

That's a shortcut for u-sub that only works in special cases. So when you use that shortcut, you _are_ using u-sub. Just like how the method of evaluating rational limits at infinity is just a shortcut for L'Hopital's Rule that only works for certain types of rational/radical functions. But yes, you're right, you don't explicitly have to do the working for it, but this channel was made for beginners.

[@VIKTORSCHAUBERGERscammersONyt]

Exactly, That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. No more unnecessary steps as part of a long and tedius process.

[@Whyyoineedahendle]

Yeah but when co efficient isn’t 1?

[@umm_mmm]

Me watching this:-😵‍💫😵‍💫

[@DeadlyBlaze]

kid named reverse chain rule then divide by derivative:

[@XanderAnimations]

derivative named kid:

@@XanderAnimations lmaoo

[@joseph_soseph9611]

u substitution is basically the reverse chain rule. The issue is that you can't just mind game your way through it like you could with derivatives except in rare cases, so you find creative substitutions and expansions and then use identities to simplify to a standard integral. This process can get very insane very quickly. If you want to see how quickly, try evaluating the indefinite integral of 1/(x^4 + 1)

[@gabrielfoos9393]

you don't even need to use substitution for such a simple problem like this, just know that for (x+a)^n, with a being a constant and n being a whole number(negative or positive integer, both work), by integrating you always get [(x+a)^n+1]/(n+1), it's just a simple derivative

[@HeyKevinYT]

i'm sorry but my inner calculus is screaming PLUS CEE

[@angelofelisimolacruz1462]

Correct. [(ax + b)⁽ⁿ ⁺ ¹⁾]′ = a(n + 1)(ax + b)ⁿ How would you answer the next question: ● Find the primitive function F(x) (i.e. F(x)= ∫f(x)dx) of f(x) = (ax + b)ⁿ (‼️whithout using the standard list of primitive functions.‼️) where x is in the Domain D ⊆ ℝ of f and n ∈ ℤ.

[@asparkdeity8717]

That is just because of the use of a U-Sub implicitly, this shows out the steps for that formula. Don’t remember a formula blindly without understanding it’s derivation

[@mainsera4407]

I’m pretty sure that’s already what U substitution is, it’s just giving a formulaic way of solving it.

[@crazyabchackerakatechanima4098]

My maths teacher always used to tell me that if it's a linear function in x then integrate it as you would just f(x) then divide by coefficient of x

[@Pankaw]

yup, because if ∫ f(x) dx = F(x) + c then ∫ f(ax+b) dx {u=ax+b, du= a*dx, dx=du/a} = ∫ f(u) (du/a) = (1/a) ∫ f(u) du = F(u)/a + c = F(ax+b)/a + c

[@thebluebeyond2329]

Some people need long solutions and some don’t. This helped with integration of (a-x)^-2. Thank you.

[@Evi19Black]

Thank you for your summary it will help me tomorrow

[@Hdbcanfb12838]

This is not speedrun this is slowwalk

[@yyyyyk]

If this channel existed when I was preparing for my calculus exams 20 years ago, I think I would have gotten much better grades!... But KZbin ITSELF wasn't launched until 2005, so KZbin didn't exist at all when I was in university. Thanks for making me feel old. 😜 No, but seriously, thanks for these videos! You must be helping the next generation.

[@Eduardo-tq5sk]

You are the good Physicist!

[@Num_nums]

Excellent explanation 👍🏽🔥

[@anonymouscheesepie3768]

(x+2)^3 / 3 + C. you dont really need to use u-sub when the inner function is linear; just remember to divide by the coefficient of the x term after integrating. since the coefficient here is 1, dividing by 1 doesnt affect the result.

[@laschelimette]

Thank you very much, I was stuck on a problem like this today :D very good short!

[@_hassannnnn]

Are you in high school?

[@alejrandom6592]

In general, integral of f(ax+b) = (1/a)*F(ax+b)

[@anori3736]

Okay so this helped me A LOT. Coming back to school (2 yrs) after being sent across seas and been thrown into a calc 2 class… I remember some things but the really helped me out!!

[@jakepanzer9643]

idk why i but i lowkey find u sub fun and interesting to learn

[@NataliesBalletFolklorico]

Thank u 😭I've been trying to figure out the step after getting the u 😭

[@andreasgschiel8111]

Me too

[@AbsoluteDementia2024]

"first we need to find you" PLEASE DON'T FIND ME!! I HAVE A FAMILY!!!!

[@ticTHEhero]

Thank you

[@LanhNguyen-ym5uf]

Using the second fundamental theorem of calculus is clearer , just find the derivative of (x+2) , which is 1 , then mould it properly. Then you get the answer

[@felixnotkjellberg]

Now integrate √(x²+2x)

[@-Accent_7]

2/3 * 1/2x+2 *(x^2+2x)^3/2

[@joseph_soseph9611]

​@@-Accent_7 that can't be true

[@joseph_soseph9611]

I just looked at the solution. That's fucking crazy. No way I could've solved that myself

[@stevhandingwall2028]

@@-Accent_7 ✅

[@ddhjcfesg456]

dx = d(x+2)=dt Int (x+2)dx = (x+2)^2/2 + const

[@karag4487]

Please make more of these

[@mndtr0]

Simplier without sub because we always can add const in differential: dx = d(x + const)

[@jonnelpamaong4825]

You're the best rapping in math explaining congrats

[@Pugoey]

Thanks!!!!

[@MaahirCodes]

U can use the reverse chain rule aswell ( faster u sub )

[@proguyz78]

U-substitution is the reverse chain rule

[@MaahirCodes]

@ yeah I’m aware but it’s a direct formula derived from the u sub

[@proguyz78]

@@MaahirCodes for (linear function)^n, n ≠ -1 right?

[@MaahirCodes]

@@proguyz78 yep pretty much and when n = -1, it goes into the ln world

[@PowerUpStudio_]

i found it before the video even started

[@IndianB787]

Bro made something so easy complicated Just find the anti-derivative then you’re done (x-2)^3 ---- 3

[@dyzphoriia]

that only works in very simple problems like this one

[@juthyzaman2675]

Ok ok i subscribed. U earned it!❤

[@Ricardo_S]

Oh I just develop the square of the binomial and integrate every term, but your metod it's Very good, if it is something basic, it should be noted that I am just learning to derive/integrate, so I don't know a lot of

[@nicholashung7871]

“I don't integrate the question, l differentiate the options” ~Ме

[@Hadeshinai1]

Wait till trigo functions get involved

[@HardstuckIronAlaynac]

It’s tough for me figuring out what “u” is

[@awvz_1194]

The multiplying of both sides by dx caused me physical pain... smh

[@leokraus8925]

Why?

[@MeAskWhy]

Everything on KZbin calculus makes sense BUT when I get in class I’m dumb 😊

[@AyeMinKhant-gd3cj]

For this specific method, we can just simply use antiderivative.

[@Zkflames]

this is the equivalent of using the definition of a derivative to solve for the derivative of x^2 lmao

[@souravganguly7537]

thanks bro

[@cegexen8191]

just expand the x+2 to get the integral of x²+4x+4

[@hydropage2855]

Not a speedrun at all. Just notice the derivative of that is 1, then treat (x + 2) as if it was what you’re integrating, and (1/3)(x + 2)^3. Should take you 1 or 2 seconds to solve

[@timwunenraged901]

yeah I'm taking AP Calc AB next year and It is wraps.

[@079sivagiriv2]

In normal way, by expanding (x+2) ^2 and integrating we get : ((x^3) +(12x) +(6(x^2))) /3 But through substitution method : ((x^3) +8+12x+(6(x^2)) ) /3 An additional 8 is coming!!!!!! Iam so confused. Can anyone explain plz 😢!!

[@jacobstarr9010]

du=dx so u sub isn’t necessary so you get 1/3(x+2)^3 +C or just expand it like normal people.

[@Don_Deppresso]

My prof will give an "❌" for that answer

[@LamiaNayrin]

Who wants to do substitution for a leaner function? 😂

[@chrissystewart6268]

I never learned this in school this is my first time

[@JakubS]

Just use reverse chain rule, and you find out that you divide by 1 (because of the coefficient of x), so you simply have to use the reverse power rule.

[@carultch]

That's what u-substitution is.

[@Tatianapastel]

Day 1: Manifesting Desire Day 2:

[@suryamgangwal8315]

I did a question like this in the same way coz my dumbass forgot there is a simpler rule for linear equation with exponents

[@ccbgaming6994]

Don’t memorize, think

[@marius4363]

or just write it as the derivate of ((x+2)^2)/2 so thats about it , u sub is used for problems that are so easy to use just directly

[@huseyinkagantoy5469]

we still can't solve the integral of some basic mathematical functions For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus

[@Deoxys_da2]

Like in chain rule in differentiation when you multiply the derivative Why not divide the derivative in integration in this problem

[@kyrosavcic7382]

Man just add one to the power and divide by the new added power man making it so hard

[@stevhandingwall2028]

Integrate partial fractions

[@inigo-montoya]

wth happened to the integral of dU? shouldn't it be (U^3/3)*U?

[@John010]

No one has ever heard of Integrate f(x) dx = Integrate f(x) d(x+a) And Integrate f(x) d(kx) = k * Integrate f(x) dx Seriously nobody???

[@Anchanix_RioClic666]

Arent we integrating the function, why are we deriving this?

[@jima4513]

why not directly (x+2)^3/3 ?

[@jima4513]

+c , ive never done indefinite, only definite

[@GurmeetSingh-k6h1n]

Math is so difficult nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai 😢

[@cloverisfan818]

Just expand the bracket and integrate lol

[@itk77]

Why is bro making this simple problem so complex? 😂

[@BabyMessi_]

to teach? imagine it was something more complex u could apply same u sub

[@daleputnam8300]

Sometimes U-sub is helpful sometimes it's superfluous.

[@jakesnake6122]

There is no need for u sub. Make the 2 a then take that number flip it as if it was a fraction and multiply it to the front. Add c ofc.

[@oppzorber]

Why use a U substitution? its a simple derivative?

[@DirkdeZwijger]

Isn't this more useful when numerator is the derivative of the denominator?

[@deutschnacharabischemgeschmack]

You didn't need the du/dx, you could directly go ahead and substitute the u for x+2 and still get the same answer at the end. You made it way more complicated than it qctually is dude.

[@420sakura1]

My fellow idiot. You need to substitute dx with du. That's why he did ask the calculation.

[@vaishalikarande3246]

Can you pls explain where did U come from?

[@420sakura1]

It's just a placeholder to make the calculation simpler.

[@vaishalikarande3246]

@@420sakura1 Thank you! Ohh so it doesn’t have any value it’s just like a bracket? (Me don’t know anything me in 8th st.)

[@420sakura1]

@@vaishalikarande3246 don't worry, you will learnt all these and more in 2-4 years. Remember the derivative and integrals by heart. It is essential in Univeruty regardless which stream you choose.

[@swati7267]

Thank you so much for your fast reply and tips 😊😊!!

[@Dajuggahnaut]

Lol just expand it and integrate each piece. Its only a quadratic, if the power was 3 or above then I would use a u sub

[@rhyscampbell8394]

I did calculus and the moment this all made sense was when I realised theirs who du de dx bullshit was what was confusing me😂

[@kawanganyirenda452]

wow.. though there's a short way out to tackle it

[@Gareth.]

Just use the reverse chain, substitution is not needed for problems like these

[@angelofelisimolacruz1462]

Question: Is the reverse chain implicitly the u-sub approach?

[@ccbgaming6994]

U-sub is the reverse chain lol

[@NapasimisOrdibarata]

(x+2)³/3 is right but not easy to calculate when x number

[@harshkumar973]

As a beginner ,why can’t we use the (a+b)^2 identity and then integrate each function separately?

[@unexpectediteminbaggingare8074]

correct, im puzzled why they have chosen this way

[@redfalconsmdx]

You can. Integral may have different forms of answers but if you were asked to find a limit. They would all be the same

[@syed3344]

U can,the answer will be the same But the susbtituing approach is simple

[@Facha115]

n i c e

[@hanskywalker1246]

Where does the two other dx in the du=dx come from?

[@hamzahwaheed9528]

Another way is reverse chain rule

[@r.p222]

X³+x²+4x+c

[@dwestria]

I sub

[@Mave-Javin_123]

How to check the answer?

[@wiseltheysay2863]

Differentiate the answer

[@KUSHAANKOUL]

linear inside so (x+2)^3/3 works no?

[@proguyz78]

yes

[@MRGamesStreamer]

Not possible this answer check differentiate the integrated answer

[@fahrenheit2101]

Plenty of alternatives. If you really wanted to waste your time, this can be done by parts.

[@proguyz78]

If you want to do a speedrun for this integral just write down the answer

[@The..introvert-r4n]

Math was easy before meeting calculas😂

[@gg-dm7te]

3) 2 (2x)dx = ∫ [ f(x)] 2 f ′(x)dx = 1 3 ∫ [ f(x)] 3 + c = 1 3 (x2 + 3) 3 + c

[@Arnav2322]

t²dt = t³/3 = (x+2)³/3

[@OmarSalah17]

why didn't you use ∫(ax+b)^n dx=[(ax+b)^n+1/(n+1).a] +c

[@soliSchuler]

Ok, this is impressive. now explain partial integration in 60s 🤣

[@Neoncoder]

Can you please tell us this real world use

[@supreemdahal4277]

(ax+b)^n has a formula use it

[@mhjk6080]

You dont really need to use u substitution in this scenario

[@jmrs_]

It's genuinely easier to just do it as it is

[@marklgarcia]

True, but this is a good demonstration of using substitution to solve the integral.

[@joesh8213]

People will hate on me for this but i do not care. I never liked U sub and never will. I understand the concept and instead just solve the integral using the tabular table instead.

[@МаксимАндреев-щ7б]

Just (x+2)^3/3+C

[@Linkirby]

Look I understand it to an extent but slow down 😂

[@Zephyr_197]

Just reverse chain rule?