The Integral of sec(x) the COOL WAY!

[@stingrayx2182]

Imagine a teacher’s face when seeing a bruh substitution on an exam answer...

[@joda7697]

The best thing is they can't even say it's wrong, even though they'll probably really want to!

[@kishorekumarsathishkumar1562]

maths: I will give you the entirety of the English and Greek Alphabet Flammy: BRUH

[@neilgerace355]

That's peak Flammy there

[@MusicalInquisit]

Don't forget the Hebrew alphabet (sometimes).

[@carultch]

@@MusicalInquisit The Cyrillic alphabet is starting to be used as variables as well. There was a Russian mathematician who coined the use of the Cyrillic letter Sha, that looks like a rectilinear W, in honor of his name that starts with an SH.

[@pedrocrb]

Ive been promissed the integral of sec(x), and got the integral of sec(t). Lies

[@neilgerace355]

Let's not have any sec(t)arian violence please :)

[@pedrocrb]

@@neilgerace355 Yeah, let's also not be sec(x)ist

[@randomguy-kt6vg]

Can't trust anyone these days

[@eva-jd2zg]

But we were given the gift of bruh substitution! dbruh4life

[@marcellomarianetti1770]

Clickbaited

[@semi8883]

9 minutes for a simple integarahl like sec(x)? This is lookin very spicy Edit: I just finshed watching. Using bruh as a substitution is the most alpha thing anyone could ever do

[@ThatGuy-kf5kc]

God damnit I'm in the middle of a lecture and I just started bursting out laughing at dbruh

[@bucsfan2565]

So this is what would happen if algebra was spelled algebruh.

[@txikitofandango]

"LOOK AT ME I CAN MULTIPLY COSINE BY SOMETHING." Multiplies cosine by something

[@technoguyx]

Ah yes, the desperate-freshman-in-the-middle-of-a-test way.

[@DarthSidian]

Final Boss Integral: "I fear no man... But that t h i n g ..." *_Flashbacks of Papa Flammy using the legendary b r u h substitution_* Final Boss Integral: "It scares me."

[@abdullahafridi6889]

Anyway, up next: proving Fermat's last theorem, the COOL WAY!

[@neilgerace355]

I have a great proof but it won't fit in the bruhgin

[@mina_mozna]

this really be a fourth of bruhcember moment

[@DemxnMNK]

so are you saying I can use bruh as my substitution on my calc final?

[@spyrex3988]

Ahh yus the only integral I always forget, thanks for refreshing my memory

[@geethaudupa8930]

was waiting for a "dBRUHgli equation" pun

[@eva-jd2zg]

"bruh substitution" is groundbreaking and needs to be in textbooks. P.S. finally got the chance just now to sit down and do the whole integral with you -- love the "elementary > pretentious" method. P.P.S. I need to practice reading English mirrored for the memes. JENS, MY BRAIN! Loved this day as I totally understood everything that was going on, as you explained it bruhtifully.

[@Neubulae]

Student: Here I'm gonna use the U-substitution to solve the integral! The integral itself: no U.

[@sergiolozavillarroel3784]

There is another way to solve it: Integral of sec(x) ln|x/2+π/4| + C Integral of csc(x) ln|x/2| + C

[@neilgerace355]

7:12 when in doubt, multiply by the multiplicative identity

[@toby6225]

Actually the most logical thing to do would be to just find the answer in your lookup table

[@bajelman]

Thanks now I have to use bruh sub in my finals soon

[@toxicara]

Have you done the Hyperbolic functions "the cool way" yet?

[@kairostimeYT]

(secx + tanx) multiplication totally has a really intuitive meaning.

[@Ricocossa1]

No it doesn't I hate it!

[@Ricocossa1]

@@alex_schwartz oh man. It's honestly the first time this happens to me. For shame!

[@Dinghly]

The method flammable used is really useful since it doesnt involve transcendental function

[@jacobolus]

It does if you keep digging into it. sec θ + tan θ is the stereographic projection of exp(iθ) through the point i onto the real axis, and has as its power series the zigzag numbers. See wikipedia: Alternating_permutation

[@Rundas69420]

Next exam, the bruh-substitution will come in handy for sure. Then, the people correcting my work will definitely have something to laugh about, besides my proofs :D

[@gustavgadehebsgaard5727]

Just found out that arctanh(sin(t)) is a valid result for this integheral, and now I never have to try and memorize this bullshit ever again

[@sdparsons]

When I heard "d bruh" it was almost certainly the first time I've laughed out loud at a calculus video, haha

[@sypherdex7513]

Amma use bruh sub for my exam tomorrow 😂😂

[@eva-jd2zg]

PLEASE tell us how that goes and if there are any "wtf" comments when you get it back but then they're like "well, it was right sooo...." FULL MARKS!

[@sypherdex7513]

@@eva-jd2zg i just found out he's a fan as well 😂😂

[@eva-jd2zg]

@@sypherdex7513 Haha that's awesome XD

[@braedenlarson9122]

Okay today class we are learning bruh substitution

[@carultch]

I want to see you use Eszett and umlauted letters as variables.

[@GoingsOn]

I’m never going to think of substitution the same way again 😂 Bruh-substitution is the best.

[@edmund3504]

bruh (keep it going)

[@GoingsOn]

Bruh

[@DarthSidian]

Bruh

[@spaghettiking653]

Bruh

[@matthewcapstick6242]

I heard someone today calling capital sigma "e"

[@matthewcapstick6242]

@@PapaFlammy69 hey what about this.. B-rho

[@eva-jd2zg]

BRUH! I have the infinite convergent series of pi tattooed under my collarbone (PapaLeibniz) and someone came up to me a few years ago and said "WOAHHHH COOL TATTOO! NICE EPSILON" and I literally face palmed. In front of them.

[@WilliamKilcrease]

I never really knew why the multiplied it by sec(x) + tan (x) until I solved it legitimately and from your video. I would just memorize all the answers to common integrals

[@RC32Smiths01]

Any integral is of interest for me, especially the cool way 😎 Awesome work!

[@RC32Smiths01]

@@PapaFlammy69 :D

[@connorr.126]

video idea: the most complicated way of finding the integral of x dx or something like that

[@angelmendez-rivera351]

Connor R Using Feynman integration hahahahaha

[@bucsfan2565]

Connor R Find integral of 2x dx

[@floreskyle1]

Are riemann sums only usable to definite integrals??

[@carultch]

@@floreskyle1 Riemann sums aren't really that useful at all, other than laying the groundwork for teaching integration. Usually, if a Riemann sum can simplify to an elementary expression, you'll be able to integrate it with standard calculus methods anyway. Simpson's Rule is much more computationally efficient than a Riemann sum, where you need to integrate numerically. It's also more computationally efficient to rephrase the integrand as an infinite series, and integrate the individual terms of the infinite series.

[@kostasDrou]

We're going to use BRUH

[@douglasstrother6584]

Papa Flammy's Quantum Mechanics! =

[@nevonitay]

at 5:30, can someone explain how the second integral is du/u if u=1-bruh then 1+bruh=2-u times dbruh is du/(u-2).. ...right? am i wrong? where am i wrong?

[@seankelly8906]

Nicely done! I love your comment about the pretentious multiplication. I feel compelled to mention that I'm sure you could do a hyperbolic substitution (Euler sub) as well, re: using the 1+sec^2. The math is entirely similar to the evaluation of the archyperbolic tangent.(Indeed, though hyperbolic trig isn't taught much, people usually do a similar pretentious move evaluating such integrals, rather than Euler sub or u sub from rotating and scaling the unit hyperbola to y= 1/x.)

[@gamma_dablam]

A nice integral for combustible bois and grills: [0, pi/2] of sin(2x)cos(x)e^(2x) I think you'll enjoy this one

[@angelmendez-rivera351]

Godwin Austen What is that notation? Is it supposed to say sin(2x)?

[@gamma_dablam]

@@angelmendez-rivera351 yes Sin(2x) It is a typo

[@tanvec]

Time to see some algebruh shirts in the papa Flammy store

[@sebastianquinterouribe368]

Thanks papa flammy, never thought of this route

[@stolenmonkey7477]

I will use a bruh substitution on my next first ever exam I am not in calc yet, I am studying ahead This is the best idea I have ever seen

[@whybeee]

br(u)h substitution Edit: Papa liked my comment. My life goal has been fulfilled.

[@That_One_Guy...]

Oof

[@fanyfan7466]

rip

[@ganeshprasad9851]

Papa... Can you please prove the Reimann Hypothesis of the Zeta function :D ? I would love to see you prove that the non trivial zeros are present on the critical line and the non negative even integers :)

[@angelmendez-rivera351]

Ganesh Prasad The non-negative even integers give you trivial zeroes, not non-trivial.

[@ganeshprasad9851]

@@angelmendez-rivera351 I m mentioed non trivial zeros only for critical line

[@alberteinstein3612]

My Calc teacher: today we are going to learn u-subs Me, who uses bruh-subs instead: I am 2 parallel universes ahead of you

[@gamingstars8956]

2:58 thw best part🤣🤣🤣

[@PapaFlammy69]

:D

[@The1RandomFool]

In addition to secant, I also have the integral of secant cubed in my head.

[@MathIguess]

Couldn't stop laughing at that substitution

[@anshumanagrawal346]

When I got first got this question as homework I used this same method then after spending sometime simplifying it, I realised if I just directly multiplied the denominator and numerator by sec + tan, the numerator just becomes the derivative of the denominator so the answer would easily come out to be logarithm of sec + tan. I thought I was a genius for figuring that out :p

[@yeremiafrans9425]

PAPA FLAMMY'S ADVENT CALENDAR (ouaiaaaaaaaaahiiije)

[@frozenmoon998]

Coolio, we are going to use Bruh.

[@nadeemhameedi1196]

Multiply and divide sect by (sect + tant) u will get sec squared t + secttant which is the drivative of sect+ tan t so u finally get Ln (sect+ tan t)+c

[@shlokdave6360]

I really appreciate what you said at the start of this video. Its so idiotic to multiply and divide by secx + tanx- its cheating. Thank you for making this one.

[@nnniv]

*_COOL_*

[@maquiavelo7157]

😳😳😳Bruh substitution!! That's amazing Is there a bruh substitution for dx/ (x^2 - 1) Instead of using x=secz method?

[@carultch]

Given: integral dx/(x^2 - 1) Factor the bottom: integral dx/[(x + 1)*(x - 1)] Set up partial fractions: 1/[(x + 1)*(x - 1)] = A/(x + 1) + B/(x - 1) Use Heaviside coverup to find A & B: at x = -1, A = 1/[covered*(-1 - 1)] = -1/2 at x = +1, B = 1/[(+1 + 1)*covered] = +1/2 Thus: 1/[(x + 1)*(x - 1)] = 1/2/(x - 1) - 1/2/(x + 1) Split the integral: 1/2*integral 1/(x - 1) dx - 1/2*integral 1/(x + 1) dx Let bruh = x - 1, and let chad = x + 1. Rewrite the first integral in the bruh world, and rewrite the second integral in the chad world. dbruh = dx dchad = dx Thus: 1/2*integral 1/bruh dbruh - 1/2*integral 1/chad dchad integral 1/bruh dbruh = ln|bruh| integral 1/chad dchad = ln|chad| Thus we have: 1/2*ln|bruh| - 1/2*ln|chad| Combine results with log properties: 1/2*ln(|bruh/chad|) Recall definitions of bruh and chad, add +C, and we're done: 1/2*ln(|(x - 1)/(x + 1)|) + C

[@MrRyanroberson1]

1:33 i don't actually know the answer to this either, so i'll try before watching. int 1/cos dt. so let's see... maybe some complex numbers? i'm bad at guessing. int 2/(e^it + e^-it) dt. not better... int 2(e^it - e^-it)/(e^2it - e^-2it) dt int 2sin(t)/sin(2t) well that was interesting. 2sin(t)cos(t) = sin(2t), derived from scratch! maybe instead a u sub is in order. u = 1/sin(t), du = cos/sin^2 dt, u^2 du = cos dt so we get: int u^2/cos(t)^2 du. but wait! cos(t)^2 = 1 - 1/u^2 int u^2/(1-u^-2) du. this looks like a job for trig functions! sin^2 + cos^2 = 1... so 1 + cot^2 = 1/sin^2 (dividing). then -cot^2 = 1 - 1/sin^2, so let sin(v) = u. cos(v) dv = du int sin(v)^2 cos(v)/-cot(v)^2 dv = int -cos(v)^3 dv. Finally! I know there's a solution in this but i tried and got a really messed up answer... I'm also pretty sure that int cos^-1 isn't the same as int -cos^3. I should get some more sleep... I swear i'm good at integrals!

[@eva-jd2zg]

Excited to watch this tonight! But Papa, don't you mean the Qool way? :P #pfadventcalendar

[@vineetkaddu1214]

Simple and Clever! Well done!

[@DevalMehtaAstrokidintraining]

In the last step, you could also have multiplied the numerator and denominator inside the logarithm by (sec(t)/sect(t)) and that would get you the usual result.

[@liroy2057]

EDIT: nvm i missed the part where you said "the same but with a +" i have a question when substituting at 5:28 why is 1/1+BRUH equal to 1/u when u = 1-BRUH if 1-BRUH = u then 1-u = BRUH then 1/(1+BRUH) = 1/(1+(1-u)) = 1/(2-u) or am i missing something

[@Otomega1]

Papa flammy: "who remember the integral of sec(x) it's fuckin stupid" Also papa flammy: "i think we have like a sec(x) and a tan(x) with a natural log somewhere.."

[@David-km2ie]

Bruh, amazing approach. Next time, you could do it with a Weierstrass substitution. Cuz, why not?

[@kurt1866]

i have a E theoretical math, in the norwegian equivelant of highschool, and i am fucking wathcing this shit rn

[@KazACWizard]

as soon as you said that a cos substitution was pointless i took the challenge. if rist let the integral be of -secx as the derivative of cos is negative sine. rewrote 1 as the obvious combination of sinx and cosx squared. then i let u be cos x therefore by using the definition of sines and cosines i constructed a triangle and rewrote sine in terms of u. then i rewrote the integral. making another substitution letting k be square root of 1-u squared. then differentiating allowed for a nice fraction. 1/(1-k^2) then by partial fractions i got 1/2ln((1-sinx)/(1-sinx)) then noting that cosxtanx is the same as sinx i rewrote. put the square root in. rationalising i got sec^2x-tan^2x which is one so i got ln(1/secx+tanx) then putting the minus back in i got the answer. a bit of a read but i think its a nice approach.

[@nicholasthesilly]

Ah yes, the dangers of sec(t)arianism

[@thepruh1151]

"bruh and bruh is going to cancel out" aight, next time someone says bruh, finna hit them with the bruh

[@Jaffa-yt1gx]

why is bruh the most stupidest shit ever but absolute gold

[@Mr35diamonds]

Will integration by bruh-substitution get me marks in my exam?

[@kishorekumarsathishkumar1562]

i mean if my math teacher used perpendicular by perpendicular x for d/dx, yes you can like the upside down T like T/Tx

[@angelmendez-rivera351]

Kishorekumar Sathishkumar Wait wtf lol

[@darkseid856]

Greatest substitution in the history of mathematics .

[@거미남자_spidy]

coool integral papa!

[@angelmendez-rivera351]

3:05 *I'm about to do what you'd call a pro-gamer move.*

[@weltkaiserendzeit2417]

Ok, the bruh substitution is a very advanced skill for pros only. But, now, time for the real challenge : Try integrating from 2 to infinity the function zeta(s)-1 ds where zeta is the Riemannsche ζ-Funktion. If you choose to do it, then good luck !

[@kishorbhushan8292]

is it bra aur something else?? 🤣🤣🤣

[@matron9936]

Alle haben für die Bruh Variable gewartet.

[@osamaattallah6956]

Man is he high🤣🤣🤣

[@vcl-eq3vv]

Wow, you solved integral of sec(x) like a absolute chad.

[@JaybeePenaflor]

Papa Flammy, you lost the perfect chance to use sec (x) in your integral.

[@BardaKWolfgangTheDrug]

awwww Papi gettin sexy handsome when he's agressive to secans *-*

[@ogorangeduck]

Best is count the squares on Desmos

[@holyshit922]

I calculated it the same way but Euler substitution fans may use sect = u - tant substitution

[@kishorekumarsathishkumar1562]

d/dn (sec(ant)/cos(ine)) i is the unit imaginary constant

[@angelmendez-rivera351]

Kishorekumar Sathishkumar d/dn[sec(ant)/cos(ine)] = (d[sec(ant)]/dn·cos(ine) - sec(ant)·d[cos(ine)]/dn)/cos(ine)^2 = [at·sec(ant)·tan(ant)·cos(ine) - i·e·sin(ine)·sec(ant)]/cos(ine)^2

[@desertrainfrog1691]

I have to say I went to go download an amogus twerk gif and it asked me if "I would like to download it *again* " Good Sunday so far also gud integral Flammerble Meff

[@thephysicistcuber175]

Will you do some complex analysis this year?

[@thephysicistcuber175]

@@PapaFlammy69 *cries in C* bruh

[@vladislav_artyukhov]

d bruh 🤣🤣

[@normmacdonaldfan]

Was so disappointed when you brought back sin(t) for all the bruhs. RIP bruh

[@deepthakur14916]

Next video integral(x^(-x),0,∞)

[@deepthakur14916]

I got heart from papa yay!!

[@zoltankurti]

@@deepthakur14916 well x^(-x) goes to 1 as x goes to infinity, so that integral surely diverges.

[@deepthakur14916]

@@zoltankurti it converges

[@deepthakur14916]

@@zoltankurti it goes to 0 as x approaches infinity

[@zoltankurti]

@@deepthakur14916 damn. 1/(x^x). Need to get some sleep.

[@tiziocaio101]

Could you do some complex analysis video?

[@FGj-xj7rd]

Ahahahah I am dead. Dude, this is so badass.

[@leftenanalim]

I know from the very beginning that you were using the Hagoromo Chalk

[@WhattheHectogon]

Oy, that weird first representation of the final answer is fyre...never seen it presented like that. Way cool brrruruuurururuhhrhhhrhaiaaiaiaioowhuweyeyhhhhh. Loving diese Advents. I've got a pretty cool video coming up after this one I'm uploading today you might find pretty neat ;D

[@hansb1337]

bruh

[@Stephmusiculture]

It was clear, thanks.

[@dcterr1]

Cool explanation but kind of a weird teacher!

[@hasoncraft4680]

Thank you bro🔥

[@wryanihad]

You can say tanh(cosx) instead of partial fraction Nice work Good for you

[@justim4545]

how does cos(bruh) = sin(bruh)? what am i missing

[@물고기-p4f]

I thought you would reveal the cooler way

[@ajaykaushal3373]

I think @MuradBashirov was here

[@eliaspelo8844]

In finnish high school's you have to take the matriculation exam for those subjects you want (min 4) (kind of like the SAT's I think). Well my matriculation exam on math is coming up in two months. The exam is really official and stuff. What do you guys think should I use "bruh" as a variable in every problem I can? That would be hella funny to look at few years later.

[@eliaspelo8844]

@@PapaFlammy69 Xdd. With Papa Flammy on my side I'll do it!! Love your content btw