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
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!
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
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🙏
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.
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😊😊😊
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……..
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...
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 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.
one time i got hit by a bus and Maths505 integrated me back to health. i owe him my life
😭😭😭
That's so nice of him, now he's my favourite after Leonard goatler
@@spinothenoooob6050 more like LAMEnard Euler hah
Hi,
"terribly sorry about that" : 1:26 , 2:21 , 4:14 ,
"ok, cool" : 4:23 , 5:11 .
I’m beginning to think you might figure out backwards time travel.
Hopefully soon
this integral uses:
•taylor series
•Laplace transform
•complex partial fractions
•digamma
•trigamma
•reflection/duplication formulas
•hyperbolic functions
or whatever the hell he did at 4:35
Missing Cauchys residue theorem
🤤🤤🤤
@@abdulllllahhh i did not use cauchy's residue theorem when solving this integral.
@@maxvangulik1988 no I’m saying the integral is missing crt to be perfect
Great video! Loved the differentiation under the integral sign (it's actually a property of Laplace Transform) 😊
this reminds of the old days where u use multiple results to make a monstrous integrals to submit to u😊😊
The way you make solving math fun is amazing
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
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!
Thanks mate
And yeah a bit of practice everyday goes a long way
@@maths_505Yeah, practice is an underrated superpower. 😃
In Germany we say: Übung macht den Meister. 😊
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
That's a good idea
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🙏
interested on this as well
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.
Exactly 💯
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😊😊😊
This has to be one of my faovrite videos of yours
It's one of my favourite integrals...little bit of everything
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……..
That is a really good theory.😊😊😊
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...
The intro voice was 😂 like Mr kamaal sobered his vocal in wine 😂😂
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)
Nicely done with health dose of tasteful subtle humor!
Jeez dude, this is art 🎨
"how long have you been staring at this"
Me: yes
Very nice! At the end it should be with negative sign -pi/2coth(pi). Oh now i saw you fixed it😅💯💯
6:55 forgot the square
As usual , just hero
Good problem!
Great video , thanks for making it
Fantastic
So nice!
What does any of this mean
pomni quote
Very nice. Thanks
how do you justify d\dk when k is discrete variable?
Treat k as continuous obviously....or just replace k by t and at the end substitute k=t
❤❤❤
What hyperbolic tan cot means?
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.
@@Grecks75 trig functions are for unit circle and similarly these are for hyperbola oh nice ,but why do we need em?
@@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.
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)
Good stuff
I think you lost a negative sign on the way but I am not sure
Okay, cool 🎉🎉
A little bit of this a little bit of that aaa video
Comment for the algorithm:
Oooookey Cooooool ❤
First time being first!
Twenty-six seconds on "like and subscribe" absolutely ridiculous