Integrals Tier List

[@Kcl-Integrator29]

For all you 🤓🤓. These techniques are from calc two and below so I don't wanna hear some very specific thing you learned for a week in complex analysis.

[@karelnarselo]

LMFAOOO

[@aimsmathmatrix]

A lot of advanced integration theory also comes from measure theory, which isn't really from complex analysis - but a course / topic in and of itself that deserves its recognition tbh

[@lih3391]

math 505 has some nice stuff, there are way more methods lol

[@Chomta]

You forgot to add that 2+2=5

[@user-mf7li2eb1o]

What is he talking about guys?

[@itsme5625]

The ultimate integration technique: Guessing

[@carultch]

That's called integration by differentiating the Ansatz. You guess the form of the integral result, with undetermined coefficients, then differentiate, and then match coefficients to the original integrand.

[@FirstnameLastname-bx4zk]

@@carultchundetermined coefficients. Like the differential equations one?

[@carultch]

​@@FirstnameLastname-bx4zk Similar to it, yes. In a way, it is a solution to a diffEQ, where dy/dx = the given integrand. Here's an example. Consider: Integral (3*x + 4)/sqrt(x + 1) dx Assume the solution has the form: (A*x + B)*sqrt(x + 1) Why? Because we know the net exponent on each x-term, must increase by 1, due to the process of integration. Had sqrt(x) been the radical term instead, it'd be an application of the power rule. This is equivalent to the radical expression moving to the numerator, and a linear expression multiplied out in front. Take the derivative, to get: (3*A*x + 2*A + B)/(2*sqrt(x + 1)) This tells us that: 3*A/2 = 3 (2*A + B)/2 = 4 Solution: A = 2, B = 4 Thus the solution is: (2*x + 4)*sqrt(x + 1) + C This method doesn't always work for integrals of this form, as they can also have inverse trig or logs as part of the solution. If that is the case, you'll have a degenerate system of equations when trying to solve for A & B.

[@plant3341]

thats called engineering

[@CalculusIsFun1]

“Hospitals rule” 💀

[@santiagoriossmith2400]

I always pronounce it le hospitals rule

[@ondrejsvihnos2311]

It actually is lol

[@Dillon12]

It's actually L'Hôpital's rule. The H is not pronounced and there's clearly no S.

[@jessebalsam6475]

@@ondrejsvihnos2311I think it’s like loe-pee-tal

[@solifa1]

@@Dillon12*S at the end has left the chat*

[@andrewmichel2525]

The most engineer video of all time

[@romdotdog]

fr tho, didn't mention anything like weierstrass substitution, riemann-stieltjes integrals, differentiation under the integral sign, sum-integral interchange, elliptic/fresnel integrals (which I concede are very engin-type integrals), residue theorem, mellin transform, green's theorem, hypergeometric series, etc. I get this was probably aimed at the calc I and II level but it's still a lot of oversight.

[@joshdeconcentrated2674]

which of these were done in calc I and II?@@romdotdog

[@jonathancamina3149]

@@joshdeconcentrated2674 all

[@romdotdog]

@@joshdeconcentrated2674 none of them lol

[@joshdeconcentrated2674]

@@romdotdog then how is it oversight for a calc II student to not know stuff from after calc II

[@kendash7286]

Love how we all agree that u substitution is the goat of integrals

[@Nzargnalphabet]

I added every trig identity I could find and wrote them down in my notes, EVEN THE TRIPLE ANGLE STUFF and therefore I am immune to trig integrals

[@cariogenic]

You can always derive trig identities with complex numbers

[@terryrodgers9560]

naw triple angles is crazy lol

[@AnIntegral]

what about quintuple angle💀

[@willclegg8191]

bro just got back from 6hours of calc and stats at uni and this video made my day

[@ceruxii3079]

Lebesgue integral > everything else

[@kwa2036]

Khinchin integral is better

[@castagnos509]

Kurzweil Henstock integral is better

[@aimsmathmatrix]

@@castagnos509Technically: The Pettis- and Bochner-integral are way superior because measure theory is, but touché on the singularity bit.

[@savitatawade2403]

differentiation better

[@doomslayer9457]

I see lebesgue integral everywhere but how do you actually lebesgue integrate?

[@安妮Bei]

This unironically gave me a much needed review on when to use each of the rules XD.

[@arkk9477]

Ultimate technique: diffrentiate the options

[@coastercookieYT]

I love these videos so much as a math nerd these are amazing. Some ranking ideas: Trig identies Log properties 12 trig functions Math courses

[@totallynotpaul6211]

L'Hôspital's rule is goated.

[@Ryan-ex1ut]

“Do not forget to substitute for dx” was personal

[@duxm8446]

You didn't include hyperbolic functions in your function video and that disgusts me

[@viefcheesecake]

Reciprocal is the same thing I think btw, he didn't forget

[@serulu3490]

The absolute value of hyperbolic functions :

[@jasimkunhi1543]

​@@viefcheesecake hyperbolic functions are sinh cosh tanh etc (made by taking averages of the exponential function) and happen to follow the same rules as trig with the difference that the pythagorean identity has - instead of + in the middle. afaik, this would make hyperbolic the same difficulty as trig its just annoying to remember which one to use depending on the sign. Reciprocal trig functions are sec cosec cot which you learn along with normal trig and arent the same as hyperbolic. You could say all of them fall into trig though

[@Kcl-Integrator29]

sorry :(

[@wolfiegames1572]

Literally just some e^x

[@Glexzy]

i know iam cooked when this videos appears on recommendations

[@RR-bs9mr]

what about feymens technique

[@instinx9154]

literally about to comment this. But technically didn't it originate with Leibnitz?

[@yudoball]

S tier

[@opawmgaming4861]

Yes Leibnitz made it but the actual improvement for practical use of the technique is done by F​eynman@@instinx9154

[@אקרמיצאלח]

​@@instinx9154bruh probably most of calc originated from him, but no one mentions him only time he was mentioned in my calc courses was in alternating symbol sums

[@07_Obi]

This only considers Calc I and II techniques. Otherwise we could go beyond S tier with techniques involving special functions and Contour integrations

[@jacobstarr9010]

Trig sub: most fun Int by parts: easy to set up with DI method u-sub; pretty goated and is pretty easy to understand Power rule: simple, however limited to simple polynomials. Partial fractions: the worst of all. Although it’s not hard a simple problem will take a long time because the fractions take a while to set up. But once it’s set up, it’s pretty easy to integrate. Improper integrals: also not that bad, just make sure you are good at taking limits.

[@sgf7647]

Never thought I would find myself here. Good vid btw

[@rexcabingan1262]

In stat, we have a very niche integration technique where if the integrand factorable into some constant and a probability density function, and the domain of integration is the support of the pdf, the integral evaluates to 1 and hence the value of the whole integral is the constant.

[@07_Obi]

Yeh thats a very niche type. You wont find integrals like that often

[@godprozee]

Only understood "pdf", the most familiar word here 😭

[@07_Obi]

@@godprozee If the integrand can be simplified into the form of a pdf (with some constant multiple) and the limits of integration coincides with the set of possible values of said pdf, then the integral evaluates to said constant. (Since the integral of a pdf gives the probability of a variable falling within a particular value, the probability of a variable falling withing the entire space/domain is 1, and hence the integral evaluates to 1 times some factored constant)

[@godprozee]

@@07_Obi uhmmm actually I was talking about the pdf file format, not the pdf you are talking about, I have no idea what that pdf is 😭😭

[@07_Obi]

@@godprozee Ah shi🤣

[@尻槍文]

I should’ve watch this before my calculus exam

[@thiagomotta777]

I put this video on watch later when i was starting calc 1, with the idea of watching it after i understand what an integral is. I just passed calc 2 and i agree with this tier list

[@skourthsgiaoyrths9610]

finding this chanel reminds me of why i left engineering school for good, thx bro

[@AJ-er9my]

One of these w/ multivariable calculus stuff would be dope‼️‼️‼️

[@xYottabyte]

Our prof made a list of order on which we would try to guess what technique is more effective to integrate. example, if we cannot do u-sub, do partial fraction, if not, do trig-sub, and the list goes on...

[@debonreepdas2265]

d(50)/dx out of 50. LMAOOOO

[@user-nu6zl6ct7w]

💀💀💀💀💀 would be funny if our profs gave us that

[@raven.petrichor]

@@user-nu6zl6ct7wimagine getting your test back and having to solve more calc problems to figure out your own score

[@Rando2101]

d50/(50dx)=1/x hmmm?

[@smbushi]

@@Rando2101derivative of a constant is always 0 and d/dx is not a fraction

[@Kier_but_who_cares]

😂😂😂 you clearly don't know the derivative rules ​@@Rando2101

[@noahali-origamiandmore2050]

Feynman's Trick: S+ Tier It is so overpowered.

[@marcocariddi5726]

i remember use residue theorem to solve improper integral that cannot be solve in real domain and feel like a pro, nowdays im practically graduated in electrical engineer and i never use it after xd

[@moving_knight]

You forgot 1/1+x^4 What a neat trick that one is

[@skittles8186]

“d/dx(50)/50”💀💀💀💀💀💀 im literally dying laughing

[@EXDGamerThePro]

Incredible List !!!

[@EXDGamerThePro]

I agree!!

[@quazar807]

Solving trig subs was always the most satisfying thing ever, even tho they’re annoying asf to me theyre s tier

[@Mostafa.Koriem]

facts

[@adreezy6576]

i thought i was the only one. so satisfying

[@MainChannel9521]

Best kind of your videos

[@randhyLeksu7288]

i love how he defend the tier list 😂🙏

[@Mave-Javin_123]

1:10 U sub is the reason I evaluated an integral in 16 seconds with no solution

[@instinx9154]

You should do King's Property, Feynman Technique, and Laisant's technique

[@nulenmaths8654]

You didn't even include the technique with the residue theorem, which is the BEST technique for integrating in 2 lines impossible integrals

[@07_Obi]

Calc 1 and 2...

[@ElusiveEel]

@@07_Obi That was never specified in title or video.

[@uncommonusername2507]

As an engineering student you sometimes see them in your dream

[@user-mf7li2eb1o]

Youll never see a violin the same like u used to as a child

[@othila9902]

Me when I have to find the area of the shape formed by erf(x) and it's asymptote from zero to infinity (pretty cool excercise imo, the answer is 1/√𝝅)

[@feliblade1694]

derivative tier list when

[@FishSticker]

They’re all s tier because they all work properly, maybe product rule A tier and quotient rule B tier

[@marrydawn5478]

Chain rule, everything's chain rule my. friend

[@FishSticker]

@@marrydawn5478 chain and power rule ftw

[@NotBroihon]

​@@FishStickerquotient rule c tier at best

[@FishSticker]

@@NotBroihon it's technically just product and chain rule though

[@saraandsammyb.9599]

Awesome vid! You should do one with advanced techniques ie. Feynman’s Technique, undertow technique etc.!

[@Nick-qv6el]

Now do linear algebra theorem tier list pls

[@IvyANguyen]

I think they forgot one: those integrals where you have 1/sqrt(polynomial) and need to complete the square on that polynomial before you can do anything else, like trig/u sub.

[@ysy7777]

What about Gaussian integrals?

[@damilarefm]

Reduction formulae is useful for integrating high powers of trig functions

[@BBQsquirrel]

U-sub is the best integral to use when you want to pick up a nerdy crush: Me: Let's do some integration by substitution Crush: Why? Me: Because I want to replace all my x's with u

[@luizalex.7424]

Feynman's trick, where?

[@albireo2990]

me, a gcse-level student watching a video about a field of maths i barely know anything about:

[@thetachyon456]

Bro didn't even bring up the hell that is Bose Integrals

[@acidicspecter]

You missed the real goat that is natural log integration.

[@carlosfelipecorreavelasco3768]

I would've included Weierstrauss substitution and places it in like Z tier

[@sebikusik]

I expected a ranking of Newton-Leibnitz integral vs Riemann, Riemann-Stieltjes, Ito integrals etc. Still cool video though.

[@romdotdog]

same, naming your channel name "integrator" is an interesting choice given the level

[@Kcl-Integrator29]

fair enough but i can name my channel whatever i want

[@Kcl-Integrator29]

we all start from somewhere

[@romdotdog]

@@Kcl-Integrator29 you're arguing with nobody at this point haha

[@Kcl-Integrator29]

👍

[@Nzargnalphabet]

I both have friends and am learning integral calculus, I therefore accept that I am insane

[@thecristelteam9217]

U-sub is absolutely the goat

[@afrolichesmain777]

Upset that integration by parts isnt S tier. IBP carries ODEs by a mile.

[@danielnelson6131]

integration by parts is goated af

[@theemminenceinshadow]

hey, i new to integral and im really confused about "is dx and du even matters in the expression" I don't get the goat integral one at all, whats happening with dx du?

[@Kcl-Integrator29]

Basically you are trying to replace x and dx with u and du to make an easier integral. Try looking up organic Chem tutor and his u substitution videos

[@nox5866]

Where is king's rule for definite integrals

[@raycotter9558]

No Cauchy residue theory, this makes the video got in to F tier

[@TschumiQu]

No Feymann's Technique?????

[@zmarc-]

what uni do you go to? i go to mcgill and what you’re saying about the courses matches up exactly with calc 2 here at mcgill. i know that these courses aren’t regulated across different unis so i was curious

[@Kcl-Integrator29]

I go to Tmu (Ryerson) in Toronto. What program are you in?

[@zmarc-]

@@Kcl-Integrator29 comp sci

[@asmrscollector]

i study in russia, it’s almost the same for me. although there are other methods, they are specific for similar integrals

[@nghiatrantrung834]

Dude, trig subs are actually one of the most practical to master when you started learning calculus. When you go further, learning about polar coordinates this shit is just trig subs on steroid but also the most practical coordinate system. So yeah,kids, do your trigsubs, it's good for you in the long run. Don't do integration by part, it's for people who can't do better form of integration

[@MinecraftForever_l]

You're as a mathemetician as my dog.

[@pequlal169]

no vector integrals?

[@M.2000-v2g]

I was telling my brother statistic is built off of calculus but he wouldn't believe me. Am I wrong or is he ignorant?

[@sumansemwal4981]

Qhat about Riemann stieltjes integral?

[@RomanNumural9]

Riemann integrals are easily F tier. Outside of a basic calc scenario, you'd see Lebesgue, Ito, or Steiljes integrals. Riemann integrals are clunky and restrictive. Also as an actual integration technique it becomes intractable pretty fast

[@user-mf7li2eb1o]

Wow wow wow 0:05 its „reverse power rule“…

[@umbranocturna6342]

What about multi variable integrals.

[@ae-parfenov]

F tier: improper integrals via complex residues

[@chrisrey0018]

so we all taking calc 2 now huh

[@maximuller5548]

Where is the feynman technique

[@macultic00]

I love hospitals rule and syringe substitution

[@curtpiazza1688]

Informative and entertaining! 😂

[@mihaleben6051]

3:04 ah yes. History repeats itself.

[@thomasgionta8388]

WHERE IS FEYNMAN TECNIQUE OF INTEGRATION?

[@zxtremedemon]

0:26 that means 0/50

[@split9853]

Bro you dont need matrices to solve that problem 4:17, hahahahahah.

[@ishansasmal4591]

you didn't include feynman's technique. An S tier, solves (some) definite integrals otherwise impossible also the king's property.

[@king_zuhair3208]

Why I'm i even here i have an electrical machines exam tommorw,i finished calculas for more than a year

[@plant3341]

No iterated integrals? Theyre funny little guys

[@biubiu-dt4hu]

no Ln rule?

[@phamnguyenductin]

S++ tier: numerically evaluating integrals

[@Vigaberno]

Only acceptable if you do it by hand

[@kstchl35]

should’ve include tabula the superior ibp technique

[@turki779]

Integrals destroyed my love for calculus 💔

[@Wannabecomahacker]

0:25 naw , not my bro getting 0 marks and glazing about it

[@superdolphin440]

I used L.H. in my high school finals exam

[@IchHeisseHeinz]

SINCE WHEN IS U-SUBSTITUTION INTEGRATION MY TEACHER TAUGHT US THAT FRESHMAN YEAR

[@quentinasparria7207]

Weierstrass saves trig integrals

[@decodax4880]

Yo I’m cooked on this exam dawg

[@maxpopkov1432]

Disappointed you did not include non-elementary integrals like integrals of e^-x^2, or cos(x^2). This does not mean there are no solutions you can find the area of non-elementary integrals using Taylor series, and integrating the Taylor series representation of the non-elementary function term by term to increase accuracy.

[@adityajha2889]

Cosx² i see some complex numbers there

[@maxpopkov1432]

@@adityajha2889 no complex numbers involved

[@Kcl-Integrator29]

I have not used those so it would not be fair of me to rank them

[@NintendoGamer789]

@@maxpopkov1432I assume you are talking about the differentiation under the integral sign ft Laplace transform solution? More often than not it is done using contour integration though

[@maxpopkov1432]

@@NintendoGamer789 no I’m talking about integrating the respective functions Taylor series expansion term by term to increase accuracy for computing area.

[@frantisekmoravec7317]

I miss this simple math

[@cozz124]

simple....?

[@TARRSS]

I like this shitpost videos of calculus

[@Gordy-io8sb]

Summations are *not important* at all. In physics, using summations can make you extremely vulnerable to flubbing lots of careful calculations. It would be ideal to substitute summations for polynomials or some other expressions.

[@Effect_channel]

"integrate 1/x⁵" 😊 "integrate 1/(x⁵+1)"💀

[@aleph-not]

But would you integrate?

[@karolissad.4270]

Nah, I'd win

[@Kcl-Integrator29]

nah i'd differentiate

[@metindemirci5251]

more tierlists URGENTLY!!!!!!!

[@bromax8686]

integration by parts is a pain for complicated shiii

[@inevitable1222]

yeah i like hospital's rule too😄

[@senatorimamoglu3888]

i hate anything in math involves trig knowledge, really hate that i have to know 10 different identities of cos2x

[@At-210]

mathematician tier list when

[@Kcl-Integrator29]

Soon

[@friendly_sitie]

naw, S tier was made for trig sub and integral by parts