That is the cleanest in-use chalkboard I have ever seen.

@Arriyad1

4 ай бұрын

And maybe he uses Hagoromo chalk.

Damn. The way you present is so smooth. I love it

You are a most gifted teacher

Me, at first: "Oh, no. This is going to be intimidating." Me, at the end: "Hey, that wasn't so bad, after all." That is good teaching.

your math is very organized and concise! loved the integration by parts table. thanks!

The integral of any inverse function: x*f-¹(x)-F(f-¹(x))+c ( f-¹(x) is the inverse function, F(x) is the antiderivative of f(x)) The integral of xe^(x)=e^(x)(x-1) So the integral of w(x) is x*w(x)-e^(w(x))(w(x)-1)+c =x*w(x)-e^(w(x))*w(x)+e^(w(x))+c =x*w(x)-x+e^(w(x))+c

We can also use the fact that the integral of an inverse function f^-1 (x) = xf^-1(x) -F(f^-1(x)) + C in this case f(x) is xe^x and F(x) is xe^x-e^x that term at the end x/W(x) is the same as e^W(x)

I just discovered this channel today, your explanations are very clear and is very obvious you have a real passion for math. Your content is amazing, please keep bringing these amazing videos

@PrimeNewtons

7 ай бұрын

Welcome aboard!

Man, I love your videos. You got a talent for teaching

@PrimeNewtons

7 ай бұрын

I appreciate that!

I recommend you to do the integral of the integral of the integral of the Lambert W function of a quadratic. Those who want to see the video 👇

@PrimeNewtons

8 ай бұрын

Haha. Nope!

@Shadowslayer6000

8 ай бұрын

@@PrimeNewtons at least the integral of the lambert of the quadratic?

@niloneto1608

8 ай бұрын

@@Shadowslayer6000 Dafuq even means Lambert W function of a quadratic? Give an example

@boost1718

8 ай бұрын

W(2x^2 + 3x -5)

@Shadowslayer6000

8 ай бұрын

@@niloneto1608 W(n, x^2+x+1) where n is an integer, I would like n to be 0 and hey you even have a solution for it !!!!!!! (just not real but COMPLEX)!

Mon cher ! Vous êtes vraiment très fort ! Et vos explications sont très claires ! Merci bcp !

Is this an ASMR math or am I missing something?

I was amazed at myself when I saw that I was able to reach it before seeing the video, but I did not use changing the variable. I used the logic that I put that W(x) is the function that connects xeⁿ to x and not vice versa, and I put an integral for x, but with dxeⁿ

It was great keep up with the good work. Am watching from Cameroon

This was quite wholesome to watch! Keep it up man!

I LOVE YOUR VIDEOS MAN, THEY MAKE ME LOVE CALCULUS

11:49 "this is you, remember", Yes! It's me! I love how you are talking to me in this video 😅

Bro got predicted, good video as always

You have impeccable handwriting.

Next video: Use the Lambert W function to show for which cases do we have x^y=y^x, when x isn't equal to y, for instance 2⁴=4² and √3^√27=√27^√3. Especially when fixing a value for one variable, like y=2, when the solutions are x=2, x=4, and x~=-23/30.

Just discovered this channel and I have to say I loved the way you explained this! I think a lot of students wouldn’t be as afraid of math if they had a professor like you, this is a marvelous integral 🙏🏻

@PrimeNewtons

7 ай бұрын

Welcome!

I actually prefer the first solution. It shows that W's integral can be expressed in a balance of arithmetic operations and their inverses. Like a who's who of elementary math showing up in the integral of a somewhat niche operator.

amazing explanation

The u-substituiton is a good idea! Another way would be to integrate by parts ∫1*W[x] dx = x*W[x] - ∫x*W'[x] dx and then rewrite W' . But your way is better.

i fell in love with your channel!

Great video

I'd take that first solution and rationalize the denominator. So you'd get x*W(x)^2 - x*W(x) + x + C Beautiful! You could factor the x to get x(W(x)^2 - W(x) + 1) + C, but I like the top one better

Great video, thanks! Methinks I should've started with the dW(x)/dx video, though.

@PrimeNewtons

7 ай бұрын

Good call!

I loved the video, awesome!!!

Beautiful work 👍👍👍

@PrimeNewtons

7 ай бұрын

Thank you! Cheers!

The mad lad did it.

Great video!

u perfect as always !!

That is really cool

Great video, and I want that cap.

Nice video!

What I found strange is that the RambertW function is also called a Productlog function. If call it Productlog, it might think it's a function created by multiplying log, so I personally think it's more appropriate to call it Rambert than Productlog.

@livikolumina5220

7 ай бұрын

Lambert, BTW The productlog comes from the fact that W is the inverse of xe^x, thus the product part of the name. Like a log, but not quite, and this specifies (very imperfectly) how

Great video veny clear and the enthusiasm is contagious. loved the music at the beginning (4:49): Is that African percussion?

Danke!

@PrimeNewtons

Ай бұрын

Thank you!

I really like your videos,are you using Hagoromo chalk?The writing looks very smooth

@PrimeNewtons

7 ай бұрын

I do sometimes.

nice! Gotta sub

@PrimeNewtons

7 ай бұрын

Thanks for the sub!

How can you integrate something that is not even a function?! What does it mean

Is there a formula for anti-derivative like the one for derivative (first principle)?

@PrimeNewtons

8 ай бұрын

This function is not an elementary function, so I have hege doubts. Never tried it yet.

@clemberube6681

8 ай бұрын

@@PrimeNewtons so there's one for elementary functions?

@fusuyreds1236

7 ай бұрын

Riemann sums

@clemberube6681

7 ай бұрын

@@fusuyreds1236 pretty sure it's for definite integral

@fusuyreds1236

7 ай бұрын

@@clemberube6681 right

Красунчик! Респект!

Nice q👌🏼

laplace transform fourier series fourier ..

Man could you integrate 3rd root tanxdx? I want to see how to do it in a simple way cuz you explain things nicely

@PrimeNewtons

8 ай бұрын

There's no nice way for that. It's messy all the way.

Please give an example for this integral... thanks

Wasen't that integration by parts leaves the last part as integral? I think the formula should ends with (...) +2e^u-integral e^u du (since i didn't do integrals for a time please forgive me if i am wrong)

Now padé aproximation for lambert function

Inetgrate W(x)^f(x) dx ; where f(x) is the gamma function❗

Why does W(x)e^W(x) return x instead of W(x)? Thank you.

Don't see any links in the description!

@PrimeNewtons

8 ай бұрын

🤥

@PrimeNewtons

8 ай бұрын

Fixed. Thanks

I used integration by parts first Int(LambertW(x),x) = xLambertW(x) - Int(x*LambertW(x)/((1+LambertW(x))*x),x) Int(LambertW(x),x) = xLambertW(x) - Int(LambertW(x)/(1+LambertW(x)),x) Int(LambertW(x),x) = xLambertW(x) - Int(((1+LambertW(x))-1)/(1+LambertW(x)),x) Int(LambertW(x),x) = xLambertW(x) - Int(1,x) + Int(1/(1+LambertW(x)),x) Int(LambertW(x),x) = x(LambertW(x) - 1) + Int(1/(1+LambertW(x)),x) Int(1/(1+LambertW(x)),x) u = LambertW(x) x=u*exp(u) dx = (u+1)exp(u)du Int(1/(1+LambertW(x)),x) = Int(exp(u),u) Int(LambertW(x),x) = x*(LambertW(x) - 1) + exp(LambertW(x))+C

It's not Lambert W function ❌ It's bprp fish 🐟 function ✅

Integration by parts is merely flipping axes. Simple. The "DI" method is an artefact.

How could you write: W(x)e^W(x)=x ? Instead it should be: W(xe^x)=x. Isn't it?

I understand that W(x*e^x)=x. But why is W(x)*e^W(x)=x?

@allozovsky

3 ай бұрын

Because: LHS: W[W(x)*e^W(x)] = W(x) RHS: just W(x)

@serae4060

3 ай бұрын

@@allozovsky ah thanks I see

I can't believe this bruh 💀

*blocked