Integral of 1/(1+x^4) by Brute-force Partial Fraction!

[@DaanSnqn]

"I want to do it my way, I don't care about your way, it's my video right here!" *- blackpenredpen*

[@DaanSnqn]

Gameboygenius You should still watch the video in double speed.

[@moregirl4585]

Double speed is usually too slow, but no higher choice ...

[@nemanjajevric198]

THIS IS DONT THAT BAD AT ALL!!

[@АлексейШубин-н8й]

Go int (1/(x^n+a^n))dx

[@chandankar5032]

I have a extremely easy method which use hyperbolic functions to determine the value of this at certain limits or even indefinite integral. Are you interested ?(you say i dont care about your solution)_(that hurts)😪

[@gustavoespinoza7940]

I love how he remade a 25ish minute video just because of that small mistake. It shows his dedication. I love how right after he gets to his past mistake he starts acting more calm like he’s finally redeemed himself.

[@mrjnutube]

He not only became calmer, but he said (rightfully so) that he'd redeemed himself (PHEW).

[@nathandaniel5451]

You literally made me double check that I didn't accidentally speed up the video.

[@zanti4132]

I was wondering if he intentionally sped the video up to impress us, so I slowed it down to .75 speed. At that speed, though, he sounds drunk, so he must really be talking that fast. Dang...

[@orisphera]

@@zanti4132 There are two ways to speed up or slow down the audio. KZbin uses the spectrogram to speed up and slow down audio, resulting in no pitch shift, but if you speed up some audio as it is usually inputted, stored, and outputted, the pitch gets higher, and vice versa

[@enverko]

I love your enthusiasm for math. Why aren't more professors and teachers like that...

[@blackpenredpen]

enverko thanks!! Dr. Peyam is definitely one as well.

[@PrincessEev]

Agh, I know, it's amazing how enthusiastic you two are. I was talking to one of my friends the other day and the only word I can really use to describe it is that your guys' energy is just so infectious; watching your guys' videos is enough to just make me smile, it's absolutely amazing. Enthusiasm makes all of the difference - my numerical methods professor always looks like she wants to go be anywhere but there in our class and doesn't really have ANY energy so I always feel like going to sleep in her class, but then I see you guys, or my foundations of math prof or my number theory prof and all of you are so lighthearted that I can actually enjoy myself. Energy and passion really make quite a difference on imparting material to people from an educator's standpoint.

[@leif1075]

@@blackpenredpen Why didnt you do partial fractions by factoring out the x^2 instead im curious? To get a product of 1/x^2(x^2 + 1/x^2)? That works too..

[@MrUtah1]

6:31 that “AT ALL” startled me

[@cristianmorales5207]

"I WANT TO DO IT MY WAY. I DONT CARE ABOUT YOUR WAY" LMAO

[@qasimsalim8230]

😂😂😂😂

[@Xpid07]

Exactly 👍

[@aldurthedrowshade]

"I'm going show you guys how to factor 1/(x^4+1)" *Initial D music starts playing*

[@cristianmorales5207]

neg atory DEJA VU

[@kevinl.3012]

MATH MATH MATH (im gonna write all the math!)

[@rajns8643]

😂😂

[@EM-gw6xn]

Thank You so much for this video. I know that making videos like this takes up your time and i'm so grateful that there are people like You that have the patience and the good will to help people like me. :D

[@Rundas69420]

Too much coffee confirmed xD

[@pranavlimaye]

Nope, *Big Asian Energy confirmed*

[@user-en5vj6vr2u]

*methamphetamine

[@gloystar]

I laughed at the +C at the end, poor +C has been waiting for so long.

[@vikashpanjiyara8847]

Another method to solve this is to multiply numerator and denominator by 1/(4x^2). Then breakfast the numerator as {1+1/(2x^2} + {1-1/(2x^2)}. This method will not require partial fractions.

[@arniie5288]

It's not fun if not

[@avananana]

I no longer have the right to say I am good at math. Ohh lord.

[@horizon210]

You are the most amazing mathematician on the internet. I can't thank you enough for the fantastic instruction you offer and the help you provide. The fluidity and speed with which you are capable of doing extremely complex problems is the most enviable thing I've ever seen. You are flat out AMAZING.

[@blackpenredpen]

Horizon thank you!!

[@eng954]

i think he is a genius. i was a tooter of calculus more than a half centuries . i easley say his iq is more than 160.

[@Max-ls2ye]

​@@eng954Genius yes but 160 is a stretch, 140 is more plausible.

[@ttouran]

Thank you for all these videos. I really enjoy watching them. I have always loved math, became an engineer, and had not seen these problems in a long time. Good to refresh.

[@Nateಠ_ಠ]

Still the best dressed mathematician on KZbin. Thanks for the awesome vids.

[@blackpenredpen]

Nate Yerger thanks!!!

[@kevinong8736]

5:47 "but I want to do it my way, I don't care about your way, and it's my video right here" made me laugh😂😂

[@sabriath]

"You guys kept telling me what to do, but I will do it my way because it's my video"....hilarious.

[@thephysicistcuber175]

This is precisely the reason we use complex analysis to evaluate integrals over R

[@blackpenredpen]

The Physicist Cuber ?

[@thephysicistcuber175]

blackpenredpen I wouldn't want to go through that mess to find the integral over R of (1+x^4)^(-1) if I knew i could just use contour integration and get the result way more easily

[@Fematika]

Well, you can't really find an indefinite form for the integral using contour integration, so this is still a necessary video.

[@blackpenredpen]

The Physicist Cuber what if I just want the integral from 1 to 2 :)

[@thephysicistcuber175]

blackpenredpen just wolfram xD

[@blackpenredpen]

It's only 2:32 am here, how about you?

[@jonathanvukaj2198]

11:39 (Europe) What are you still doing so late ?! Go get some sleep !

[@AlfredPros]

It's 4:40 pm here

[@thephysicistcuber175]

blackpenredpen 11:32 A.M. at the time you wrote the comment

[@blackpenredpen]

Dracquiteur I wanted to get this done and uploaded! :)

[@blackpenredpen]

The Physicist Cuber just now. Which is about 2:44am now.

[@robert_wigh]

OMG, when I saw that system of equations thought it was going to take a very long time and be hard, but you're way of handling it is just genius. It was so fast. Wow...

[@MC_Grenada]

It's 10:38 am here, also I like the supreme garms you wear in your videos

[@blackpenredpen]

thanks!

[@nightmare9566]

6:22 wasn't that a bit overkill? You had: √2B - √2D = 0 B + D = 1 Couldn't just set √2B = √2D B = D 2B = 1 B = D = 1/2

[@blackpenredpen]

Bosk Boskson love it hahahahahaha

[@nightmare9566]

Haha :)

[@PrincessEev]

I honestly thought that was more a part of his whole "I'mma do it my way not your way" thing. Which is all good: so long as the steps and result are justified and make sense, anything goes.

[@nightmare9566]

I know, I just copy pasted my exact comment from the last video, just changed the time....Just to trigger him a bit ;)

[@blackpenredpen]

I remember your comment Bosk. That's why I laughed. Plus, I wouldn't use the word "trigger". Since I usually find it really laughable (instead of getting mad or triggered) when people comment on my vids about what to do. Thus, thanks for making me laugh, twice. That also gave me the idea to say the line that Daniel mentioned. Btw, it's all good. Some of my viewers are 12 anyway. : )

[@Lily-zd6dx]

"I want to do it my way i don't care about your way" so inspiring!!

[@andrewsvideos301]

"AT ALL!"

[@wduandy]

Steve why were you triggered on this video? =(

[@mohan153doshi]

awesome speed - and infectious enthusiasm. You make calculus a pleasure - thanks bprp for this awesome integral :)

[@InvitingShores]

I felt going crazy and watched it in double speed. I'm a hero!

[@codexcursors]

5:46 "But I want to do it my way. I don't care about your way. It's my video right here." Goddamn menace.

[@bm-br3go]

Very nice! It's interesting that you can get a formula for the antiderivative of this function. A lot of rational functions like this can't be integrated by normal means and require complex analysis to compute.

[@bp-vk4vq]

Your way of teaching makes a person to listen . So good

[@stevenmoore2726]

WHEW!!!! My heart is racing 100 mph!!!

[@blackpenredpen]

: )

[@pedropiata648]

Imagine doing all of this to realise that you forgate a x on the top

[@democrateur]

that's equal in more compact form, if you check and prove, to: =1/2√2 ( acoth 1/√2 (1/x+x) + acot 1/√2 (1/x-x) ) + C ;

[@RiteshNEVERUNIFORM]

I was searching for quicker way for algebric twin questions for my entrance exam and found this with "fast" in thumb nail. Yes it was really fast 😂

[@sanchitadash8838]

🤣🤣 yeahhh

[@JustinSuperRulez]

Massive respect for doing it from scratch again!

[@blackpenredpen]

AcidicAlkali thanks!!!

[@mdmustakalamalam2650]

Thanks a lot for understanding this question.

[@jennyispoop4]

LMAO I never thought I'd love a math tutorial vid so much

[@blackpenredpen]

I never thought I'd love a comment this much too! thank you!

[@mihaiciorobitca5287]

Who is LMAO ?

[@Nothing-pg9qc]

This is how bprp fast began :)

[@The_Shrike]

6:32 I love how angrily he says “at all”

[@peterfireflylund]

This channel has the best meth videos on the internet. (Your accent gets a lot stronger when you speak that fast + it already requires quite a lot of mental processing to compensate for a Chinese accent if one isn't used to it = aaargh!)

[@AstroHolden]

Maybe it's just me but I didn't have a problem understanding his accent (I am in mid-US) although, since it was a bit rushed, I need to listen through a couple of times to digest the flood of information. However, I'd have to go this fast in an exam, so...

[@peterfireflylund]

Not a lot of English speaking Chinese in Continental Europe... Not on TV, either. A Chinese accent means almost all word endings (and syllable endings) get cut off -- which is problematic for Indo European languages because that's where all the inflections are. He did okay in another video where he spoke slower. He did that video in Chinese, too, which I surprisingly understood a bit of. The first part of this video was harder for me to understand than his video in Chinese! (I used the Hello Chinese app to learn some very basic Chinese.)

[@lucafenech269]

A living legend 😍

[@raman8535]

So good bro!!!!! Thank u for solution

[@dwipshekharmondal3877]

And in 12th grade they give us only 4 marks for this type of long ass integration . Smh

[@themohitsharma9618]

Deep Mondal its very easy

[@iumaiiumai5402]

This guy is legend.

[@adrianaguilar31]

¡¡No maa, neta eres de lo más chingón que pude haber , muchas gracias!!

[@jonnoring7225]

I'd have to specifically explore it, but the two natural logarithms can be combined, and the two arctangents can also be combined although there are minor problems with respect to x-values.

[@surajgupta2443]

This was the best thing today i saw in youtube.. it was simply too goood.. thnk u blackredpen

[@alexsere3061]

You can also factorize it as (×^2+i)*(x^2-i)

[@meat55]

This is the first time I'm frightened by a bprp video

[@Alisssap]

Faaast I like it 👍🔥🔥

[@JK-qy8le]

Watchout at 8:20 complete the square the correct result is not (1/sqrt(2))^2 but (1/2*sqrt(2))^2=(sqrt(2)/2)^2

[@alberteinstein3612]

I’m literally speechless... You are literally the smartest math person I’ve ever encountered

[@gopalrajpurohit8016]

Ok dumb albert

[@lightspd714]

You are amazing. Thank you for this and other quality math videos!

[@thenvmeguy]

i got this GODDAMN integral in my exam......and only after the exam YT is suggesting me this vid.....

[@DeluxeWarPlaya]

the gangster way

[@iaagoarielschwoelklobo6342]

18:02 The happiness of finishing this integral

[@xxgoku7774]

06:33 HOLY I FELL FROM THE CHAIR

[@mussu245]

Thanks sir it helps me a lot

[@ferrumarctus]

Genius. ABSOLUTE GENIUS. That's what you are.

[@actualRocketScientist]

Dude how do you have so much energy you sound like you drank a pack of Red Bull right before doing this LOL

[@george06sp11]

This guy is such a beast

[@NirbhaySingh-ox1jj]

Thanks sir for your valuable work.

[@gzizou_seif]

Our calculus 2 teacher gave us this as a homework , thank u very much

[@DepressionVarietyVlog]

your videos make math look really fun again...

[@gordonchan4801]

04:11 ~ 04:43 (from transcript) "and now let's combine all the x squared term namely we have this right here let's just put on the liner this until I got this and then this is another two right here right so we have this Plus this Plus that but that's that sorry this minus this and the plaster a plaster right so in total we have to a minus square root of 2 C and a plus B plus D oh this right here is the coefficient of x squared on the right hand side but once again we don't have x squared on the left hand side that means oh this has to be 0 that's good"

[@continnum_radhe-radhe]

You are awesome 🔥🔥🔥

[@davidkemball-cook559]

Brilliant, thank you!

[@bhabendas4553]

thank you for your answer

[@keeganmclaughlin8312]

This was so hard! (Even though I was doing this, but at times, I was SO FAR BEHIND that I had to pause the clip just so I could catch up with you!) (BTW, I posted this from Iowa at 5:15 pm Central Time.)

[@blackpenredpen]

Ah I see. It actually took me a loooooooooong while to practice this integral before I could record. Happy Thanksgiving Keegan.

[@sandeepsahanicodes]

lots of love from india. keep solving such problems in your own ways.

[@ysfy5106]

He went savage AF at 5:45 xD

[@joseph_soseph9611]

I had to do this exact integral as uni homework last week. Let's just say it didn't go well, but I was so frustrated that I couldn't solve it, that I spent two hours with wolfram alpha yesterday trying to understand the solution. What I still don't get is how I know which approach to take. It feels like there are so many different ways to go after the partial fraction with this integral.

[@adriellemannrich2078]

you're amazing!!!! i just wanna say thank you

[@subversively6680]

Wow, you redeemed yourself by the most aggressive beautiful fast way, GOOD WORK

[@furkanoner5558]

Good idea to calculate this integration

[@Adi-uw8zw]

@blackpenredpen you are the best

[@alejrandom6592]

"If you talk fast enough or work fast enough this isn't that bad AT ALL" ♡

[@aaronstone0758]

11:19 Did he make the same mistake twice? Either way, thank you for the video, you're making me want to do some integrals again.

[@johannbauer2863]

idk why, but its one of my favorite videos on this channel...^^

[@blackpenredpen]

Johann Bauer thanks!

[@sabilal-rashad]

Thank you so much for this awesome explanation!

[@josda1000]

blackpenredpen what is your name?! I've been looking for it. You're bringing back the passion i used to have for math :)

[@douro20]

Prof. Steve Chow, M.Ed.

[@markmitchell6098]

@@douro20 Dude you can't just dox people like that

[@DougCube]

This was very enjoyable to watch.

[@huidongzhou1669]

Good work, clear and efficient. saved a lot of time for me from tedious hw in which sense you are saving life. ^^

[@huidongzhou1669]

www.quora.com/What-would-be-the-integration-of-frac-1-1-x-4 this one only take you 2min, im saving life now^^

[@coldmash]

very nice explanation!

[@blackpenredpen]

coldmash thank you

[@ReubenMason99]

15:16 "the gangster way"

[@orisphera]

In Russia, they usually put square roots in the numerator. The number 1/(2√2)=(√2)/4 is shorter this way

[@OnlineMathswithLeepharcyB]

thanks for your help sir.

[@allenmuller795]

Well done, it is amazing

[@mariamotaku8975]

IDK why but ur just soo lovely

[@farhansadik5423]

my brain melted during 13:47 . what the fu-

[@OonHan]

Programmers: Brute Force is so inefficient, DONT USE IT BPRP: Hold my worksheets

[@JSSTyger]

If you play this at 2x speed, he turns into Chuck Norris.

[@SanjayKumar-nt6hd]

Very awesome video.... Thank you!

[@kaushikmanna4002]

Your work is fine in terms of getting a process that the integral is solvable. I appreciate it but, this problem has a very short and delicate solution with fewer steps of computation.

[@surajgupta2443]

Seriously.. it was tooo goooood

[@williamnathanael412]

Excellent video! Btw, just suggesting, what if we multiply the last 2 natural logs together, creating that x^4+1 thing?

[@ohmpi8639]

Very good solution indeed.

[@link_z]

Fantastic video as usual! I have a (probably silly) question. How do you know, in the partial fractions, that the numerator is a first degree polynomial (Ax+B) and not any other degree? Thanks in advance!

[@Bignic2008]

Not a silly question at all! Notice that the denominators in the two parts of the partial fractions were quadratics, i.e. of degree two. That means that the numerator is exactly one degree less, so you need a degree one polynomial as the numerator. If the denominator happened to be a third degree polynomial, then you'd need a second degree one in the numerator, so something like Ax^2+Bx+C.

[@link_z]

Reflective Ducky Really well explained. Thanks!!!

[@arshparmar5662]

Bro u r the best. If I were in your school, I'd be in your gang

[@dyyno5578]

man i like your videos even in vacations XD