A mesmerizing calculus journey

[@Slopynthia]

one time i got hit by a bus and Maths505 integrated me back to health. i owe him my life

[@maths_505]

😭😭😭

[@spinothenoooob6050]

That's so nice of him, now he's my favourite after Leonard goatler

[@unholycrusader69]

​@@spinothenoooob6050 more like LAMEnard Euler hah

[@CM63_France]

Hi, "terribly sorry about that" : 1:26 , 2:21 , 4:14 , "ok, cool" : 4:23 , 5:11 .

[@richierob62]

I’m beginning to think you might figure out backwards time travel.

[@RealQinnMalloryu4]

Hopefully soon

[@maxvangulik1988]

this integral uses: •taylor series •Laplace transform •complex partial fractions •digamma •trigamma •reflection/duplication formulas •hyperbolic functions

[@maxvangulik1988]

or whatever the hell he did at 4:35

[@abdulllllahhh]

Missing Cauchys residue theorem

[@spinothenoooob6050]

🤤🤤🤤

[@maxvangulik1988]

@@abdulllllahhh i did not use cauchy's residue theorem when solving this integral.

[@abdulllllahhh]

@@maxvangulik1988 no I’m saying the integral is missing crt to be perfect

[@doronezri1043]

Great video! Loved the differentiation under the integral sign (it's actually a property of Laplace Transform) 😊

[@ARUPBERA-ky6mq]

another method can be by assuming a function in alpha :cos(alpha x)ln(1-e^-x)dx from 0 to infinity and then expanding series of "ln(1-e^-x)=summation of (e^-x)^r/r where r ranges from 1 to infinity using this to get to a function a which i calculated using integartion by parts and it simplifies as a cool result 1/(a^2+r^2) and then differrentiating the function with respect to a and putting a=1 we get the same result

[@aravindakannank.s.]

this reminds of the old days where u use multiple results to make a monstrous integrals to submit to u😊😊

[@SkEi-y3b]

The way you make solving math fun is amazing

[@AlexGNR]

The fact I could follow you both scares me and makes me feel super smart for some reason. A bit of practice and I might just be able to reproduce these things. Love your video's mate!

[@maths_505]

Thanks mate And yeah a bit of practice everyday goes a long way

[@Grecks75]

​@@maths_505Yeah, practice is an underrated superpower. 😃 In Germany we say: Übung macht den Meister. 😊

[@raghavendraPi]

Nice one Bro, a request , while starting the solution could you elaborate a little more on thought process, what propped into your mind and why you rejected that. An intuitive feel for the problem basically

[@maths_505]

That's a good idea

[@augustuskaufmann7263]

how did you become so good at this? what books did you read (or other resource) to learn all these integration techniques and strategies? I haven’t seen any of this in a calculus textbook. Thank you so much, and great video as usual🙏

[@julioguilarte9438]

interested on this as well

[@daddy_myers]

It's quite simple. There is a direct linear relation between a) fucking around, and b) finding out. I'm sure you can see where this is headed, but in short, you just fuck around and find out.

[@maths_505]

Exactly 💯

[@spinothenoooob6050]

I believe that it's practice, if you always do integrals all the time(like me), you would just do it instinctively when you look at the integral(from my own experience). For example, if in my 12th grade(last year) my tr asked int_0-1 (cosx + sinx/1+sin2x)dx then I will solve it in like 4mins max and spelled the answer "ln(sinx + cosx)". I started learning calculus at the end of 11th grade but practice and my love towards maths. I think he is experiencing the same feelings as me😊😊😊

[@AA-ou1vi]

Nicely done with health dose of tasteful subtle humor!

[@Nottherealbegula4]

This has to be one of my faovrite videos of yours

[@maths_505]

It's one of my favourite integrals...little bit of everything

[@giuseppemalaguti435]

I=-2(1/4+1/25+1/100+1/289+1/676+1/1369+1/2500......=-0,61367...ho usato lo sviluppo di ln(1+x) e sinx=Im(e^ix)

[@AyushRajput-xw2ru]

The intro voice was 😂 like Mr kamaal sobered his vocal in wine 😂😂

[@RBRB-hb4mu]

I’ve solved Einstein’s “Spooky Action” entanglement riddle. Space is being pressed up into your face creating the illusion of time. Time is but an illusion……..

[@spinothenoooob6050]

That is a really good theory.😊😊😊

[@mathscribbles]

Jeez dude, this is art 🎨

[@maths_505]

"how long have you been staring at this" Me: yes

[@AA-ou1vi]

5:19 “First we need to figure out a way to get a square around this thing and that’s pretty easy. All we have to do is to differentiate” All ways differentiate! Questions later...

[@yoav613]

Very nice! At the end it should be with negative sign -pi/2coth(pi). Oh now i saw you fixed it😅💯💯

[@waarschijn]

6:55 forgot the square

[@achrafhattafi4698]

As usual , just hero

[@slavinojunepri7648]

Fantastic

[@turtledudes3843]

Good problem!

[@MathPhysRadi]

Great video , thanks for making it

[@anapotheosis]

What does any of this mean

[@maxvangulik1988]

pomni quote

[@xenumi]

So nice!

[@ericknutson8310]

how do you justify d\dk when k is discrete variable?

[@maths_505]

Treat k as continuous obviously....or just replace k by t and at the end substitute k=t

[@MrWael1970]

Very nice. Thanks

[@Kanekikun007]

What hyperbolic tan cot means?

[@Grecks75]

Hyperbolic functions, never heard of? Those are elementary functions, very similar to their circular counterparts (sin, cos, tan, cot, sec, csc), but they work with the (unit) hyperbola instead of the (unit) circle. For example, they can be used to parametrize hyperbolas, and they have very similar properties to the trig functions, albeit with small differences. For example, "Pythagoras' theorem" for hyperbolas reads: (cosh(x))^2 - (sinh(x))^2 = 1, compared to (sin(x))^2 + (cos(x))^2 = 1. Very interesting functions, in many respects.

[@Kanekikun007]

@@Grecks75 trig functions are for unit circle and similarly these are for hyperbola oh nice ,but why do we need em?

[@Grecks75]

@@Kanekikun007 As I said, they are used geometrically with anything related to hyperbolas, but they also turn up in almost every other part of mathematics, just like the trigonometric functions. They also play an important role in physics, in Special Relativity.

[@anonymous_0416]

sinh(x) = (exp(x) - exp(-x))/2 cosh(x) = (exp(x)+exp(-x))/2 tanh(x) = sinh(x)/cosh(x) Coth(x) = 1/tanh(x) Cosech(x) = 1/sinh(x) Sech(x) = 1/cosh(x)

[@spinothenoooob6050]

❤❤❤

[@yurfwendforju]

I think you lost a negative sign on the way but I am not sure

[@SanAleksiusII]

Good stuff

[@Leonhardeuler2219]

Okay, cool 🎉🎉

[@zubii2017]

A little bit of this a little bit of that aaa video

[@sethdurais2477]

First time being first!

[@biscuit_6081]

Comment for the algorithm:

[@albert3344]

Oooookey Cooooool ❤

[@zamplify]

Twenty-six seconds on "like and subscribe" absolutely ridiculous