This integral is RIDICULOUS

[@ahmada636]

I love when Kamal just gets an existential crisis mid recording

[@shivamdahake452]

I am in grade 12 preparing for JEE advanced and everytime I watch your videos I lose you on stuff like zeta and gamma functions. But I still watch your videos cause they give me a good idea on when feynman's technique or partial fraction decompositions are useful, or when substitutions that to the normal eye don't make sense, would actually prove extremely useful. Also your videos are entertaining in a wierd way, I like the way you explain the integrals. Thanks for the quality entertainment. Eid Mubarak for the next week my guy.

[@satyam-isical]

Same bro 😍

[@maths_505]

Khair Mubarak bro

[@Aditya_196]

​@@maths_505umm u Indian bro ?!

[@maths_505]

Nope. Right across the border in Pakistan.

[@Aditya_196]

@@maths_505 oh great! Neighbours

[@cadmio9413]

<a href="#" class="seekto" data-time="1178">19:38</a> I was fully sure you would say "... as we progress into madness", but thats fiiiine

[@MrWael1970]

Thank you for your featured effort.

[@renerpho]

As we've recently learned from Veritasium, 37 is the most random number. I am not surprised at all that it makes an appearance in your video just days after learning that it is everywhere once you start looking for it. 432 is a number that makes frequent appearances on certain... how shall I describe them... fringe music theory channels? Some of those would proudly call themselves "math channels", I guess.

[@sergiovigano456]

<a href="#" class="seekto" data-time="323">5:23</a> me: hell yeah G is gonna come out <a href="#" class="seekto" data-time="459">7:39</a> me: oh..

[@lyonkang7402]

I like that you’re throwing jokes into these lol

[@marcellomarianetti1770]

Well, in projective geometry there are quite a few of these completely random numbers popping out. You are working in a totally abstract theory with 0 numbers while suddenly you run into like 27 or 84, I remember kinda bursting into laughter when I was learning these theorems in class

[@krisbrandenberger544]

@ <a href="#" class="seekto" data-time="1158">19:18</a> The coefficients of the first two integrals need to be doubled in order to get to the final answer.

[@AB-nu5we]

So, you never talked to your mom? That's tough bro.

[@keyaanmatin4804]

a challenge for you. try not to invoke the beta or gamma functions at all for a whole video....

[@maths_505]

Challenge accepted

[@renerpho]

@@maths_505 Do it for an integral that screams "GAMMA FUNCTION" at you.

[@maths_505]

@@renerpho aight 😭😭

[@hassanhassane3663]

Amazing! I love the way you solved it thank u

[@aravindakannank.s.]

​​@@maths_505 now Im getting it , why in ur recent video u didn't use the gamma function 😂

[@edmundwoolliams1240]

This integral felt so much more grindy than your usual videos where you use Feynman trick or something then it pops out immediately. Perhaps this is why you had such a strange result!

[@buchweiz]

There was this video about 37 being everywhere recently from Veritasium. Although admittedly, I haven't watched it. Can't think anything about 432 though.

[@MathFromAlphaToOmega]

Here's one: If you take a sequence with with a_0=1 and a_n=a_(floor(n/2))+a_(floor(n/3))+a_(floor(n/6)), then a_n/n tends to 12/log(432). That sequence shows up in an interesting paper of Erdős.

[@ostdog9385]

​@@MathFromAlphaToOmegamichael penn did a video on it

[@mikecaetano]

There's some hokum out there about the positive health effects of music where the instruments have been tuned to the "natural frequency" of432 Hz rather than 440 Hz. But the evidence is thin. Adam Neely examined the "natural frequency" premise in a clip four years ago and found it wanting.

[@JXS63J]

As to talking to women, start with asking the time. Pick a nice looking - or desirable in your eyes - woman, and just casually ask her the time. Don't do this while wearing a watch. A long time ago I found myself standing right next to an absolutely perfect woman for a few moments who was with her bike. As she finally got ready to leave, I finally just said "Nice meeting you." She laughed because we both knew what we were both thinking for those few moments. Oh well! Thanks for the memory! A good post otherwise, and good luck to you! You do know Calculus! Maybe some woman some where appreciates that. You only need one.

[@CM63_France]

Hi, For 37, yes , it is supposed to be the number that people chose most of the time when you ask : chose a number between 1 and 100. For 432, I don't know. Hi, "ok, cool" : <a href="#" class="seekto" data-time="25">0:25</a> , <a href="#" class="seekto" data-time="66">1:06</a> , <a href="#" class="seekto" data-time="202">3:22</a> , <a href="#" class="seekto" data-time="318">5:18</a> , * , <a href="#" class="seekto" data-time="594">9:54</a> , <a href="#" class="seekto" data-time="711">11:51</a> , <a href="#" class="seekto" data-time="963">16:03</a> , "ok, great" : <a href="#" class="seekto" data-time="959">15:59</a> . * : There is another "ok, cool" between those two but I lost the track of it.

[@maths_505]

Thank you my friend.

[@vascomanteigas9433]

Apply the variable substitution x = arctan(t), and that are converted to the integral log(t)/((1+x^3)*(1+x^2)) from t=0 to Infinity. This integral can be tackled with the Residue Theorem, just use the keyhole contour integral of (log(z))^2/((1+z^3)*(1+z^2)) at compute all five residues due to five poles at z=I,-i,-1,1/2+sqrt(3)*I/2,1/2-sqrt(3)*I/2 Once made all calculations, it gives -37*pi^2/432

[@nightmareintegral5593]

I love residues!

[@maxvangulik1988]

-pi^2(1/72+1/96+1/27) =-pi^2(4/288+3/288+1/27) =-pi^2(7/288+1/27) =-pi^2(21/864+32/864) =-53pi^2/864 uhhh

[@fikretefera2106]

You love power series & Euler Mascoroni constant.

[@UnknownGhost97]

I do need to learn this

[@alelcruk]

<a href="#" class="seekto" data-time="351">5:51</a> Wasn't the target integral twice the green integral you ended up having the -37π^2/something ?

[@aravindakannank.s.]

no bro the limits are different be careful next time

[@zunaidparker]

<a href="#" class="seekto" data-time="443">7:23</a> holy shit I was NOT expecting to be called out 😂 And nah, I wouldn't call out sloppy notation, only actual errors or incomplete answers. <a href="#" class="seekto" data-time="550">9:10</a> Sounds like someone is fasting VERY hard 😂 F Eid Mubarak for next week Inshallah

[@maths_505]

Khair Mubarak my friend

[@ElMehdiBelhaj-wp9sj]

Hey from where did u learn integrals espiscally the part of beta zeta and gamma functions...

[@boltez6507]

Dude did you really did those partial friction calculations so fast or was it precalculated?

[@maths_505]

Obviously precalculated bro 😂

[@abdulazizhamid1607]

I learned I still have a lot to learn in Math

[@holyshit922]

I can convert this integral into sums I expressed rational (1-x^3)/((1+x^3)(1+x^2)) as sum (Ax^2+Bx+C)/(1+x^3) + (Dx+E)/(1+x^2)

[@UnknownGhost97]

Hello can you send me this questions or materials for this type of questions

[@SuperSilver316]

Bro pls stop me from using Contour Integration on this one please

[@NikitaMelik-Marutov]

Hello everyone! Could someone please help me with understanding, how we can write 1/x instead of x? It has to be 1/t, no? How we can change the variable in a such way?

[@Akhulud]

the name of the variable does not really matter, think of it as writing it 1/t, then putting an x instead of the t

[@tom43x34]

x is a dummy variable, you can name it whatever.

[@A_doe_wasting_her_life]

Just talk to them 😭. They are people you can talk about common interests or simple small talk the same way u do with a man.

[@giuseppemalaguti435]

Ho usato t=tgx,poi la funzione beta e gamma,mi risulta (-2/27)π^2...ma non è corretto

[@gabrielporras8294]

Hi. Can you solve this ? ... int (x^-1 In(1+x^2))dx

[@Haxislive766]

<a href="#" class="seekto" data-time="560">9:20</a> moye moyee😂

[@_ccinfinity]

Bro what note taking app do you use?

[@aravindakannank.s.]

Samsung notes bro

[@narendrapratapsinghsengar5030]

For some reason if you apply the king's rule. And add the original and the another equation which you get by applying king's rule you actually get a 0, which should be the value of the integral.

[@rafiihsanalfathin9479]

You forgot the tanx in the denominator became cotx too

[@shivamdahake452]

Talking to women makes you better at talking to women, but the degree of improvement depends on how much you are willing to make a fool of yourself. Trust me I know 😂😂

[@srikarb3350]

ohk cool 🗣

[@xdShaty]

F

[@gtensor]

Okay, cool! It's usually women who talk to me, maybe why? 🙂

[@syedabansafwan8128]

F

[@aravindakannank.s.]

F

[@txikitofandango]

F