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Is this actually Putnam level? This is ridiculously easy, had to solve this in my mid tier engineering school entrance exam in France

why did you put (1+x^2) in the exponent and denominator? I didn't got it

too easy!

Nice, sir. S Chitrai Kani

Nice video ! I really liked it ! But OMG what are these comments ? Most math videos have music in the background and most of the time it’s louder than here. Do you guys write such comments on 3b1b videos ? If Chopin distracts you SO much, then you may be the problem, not the author of the video. Concerning Feynman’s Technique, everyone knows that he didn’t invent it but that’s how we call it today. If you get so mad for someone calling this technique Feynman’s Trick, then be as mad if someone talks about the Pythagorean Theorem (which was known centuries before Pythagoras), get mad if someone talks about Fourier Series or Fourier coefficients (Euler found them 30 years before Fourier), get mad if someone talks about Riemann sums (the concept was already well known and used since Leibniz but also by Cauchy who, before Riemann, defined the integral for continuous functions). Again, concerning Feynman’s Trick, the goal is not to understand where the function f comes from, this is not a lecture where you need to be able to do the same on the exam, the goal is just to show another way of solving the integral. Everyone knows that the usual technique for this integral is easier. The goal is not to present an easier technique but simply another technique than the usual. Again, thank you for the video, I really liked the explanations and you made every step very clear. Thank you !

Not quite sure why you can shove (1 + x²) in 2 different places without explanation. Haven't done maths in 20 years, but it seems odd.

i didnt knew this was possible omg

this doesnt work for 3,4, or any number greater than 2, why? why is not possible to express gamma(1/4), gamma(1/3) in terms of known constants or bessel functions

A level students: 💀

Great video but I think at 10:50 you forgot to multiply all the numerator, so It turn out to be 5sqrt(5) + 25 and not 5 + 5sqrt(5)

Even function on interval symmetric around zero Expand cosine as power series Change order of summation and integration Use substitution to get Gamma function or integrate by parts

You just skipped the hardeset part of proving the gaussian integral. I watched to see how you proved it, but I was disappointed.

wow

Love it!!!!

You solve the problem ecactly how I think one has to do it!

impressive

amazing!!!!😊

I hope you guys like this style of video as opposed to my usual style :) don't forget to like and subscribe

Cool video

He’s back !

Seriously keep doing what you’re doing. The content is great. Your explanations are easy to follow and I thought it was a super fun video. I don’t mind the music at all. Everyone is being too pedantic either about the music or about the math but both are great and in combination even better. Keep at it! Loved this video.

HELL YEAH!

太麻煩的解法，有更快的

What about the indefinite form?

Elegant!

The Feynman Technique is actually the Leibnitz Method,; it was invented by him during the time of Isaac Newton.

Could you please turn the music up and change the style to heavy metal?

claire de lune

Nice video. Additionally I learned that u = k under the rapid handwriting approximation.😂

Thanks. It is about artificial because the derivative of arctan is used in f function. But thanks.

do this intetrals really converge? isn't it just a principal value?

Keep the music it's absolutely great really adds to the video

When I heard Ballade 1 I thought I had another tab open, but it turns out that you have executed the amazing idea of allowing us to ascend even more than when we follow along with the maths...

i love u

The result can also be written as 1/2 (arctan[x/(1+x^4)^(1/4)] + arctanh[x/(1+x^4)^(1/4)])

wtf does any of this have to do with Feynman lmao?

You can just square and change it into polar coordinates

polar coordinate is much easier.

At timestamp: 12:45: u = positive infinity since ln (0) = - infinity

do the limits not flip when we take out the -2*e^(-a^2) at 10:48

Could you solve the integral of e^-x^3 zero to infinity?

Awesome evaluation. Really enjoyed this video.

Thank you

theres no way this was a google interview question, we studied this exact integral during highschool

wolframalpha gives 1.29129 for the final sum and 1.29128599706266... with an offer to show more digits for the integral.

A v upside down is an n???

What is the source for this solution? You and someone else have the exact one, identical to the line, so I was curious if it is in a textbook somewhere.

Feynman was a very sharp cookie!

nice! By the way, what’s the song in the beginning?

no wonder this is the hardest question in google interview, no one is expecting to be asked integrals when they apply for a job at google