Remarkable use of Euler's formula to simplify the integral! But it seems to me like it would be easier starting at 6:00 to just expand e^(i sin x) into real and imaginary parts. It is then easy to find the imaginary part of the product of the three factors, which is what the integral equals, because Re{z/i} = Im{z}.
Such a beautiful evaluation and solution development. It has been a while since I have seen such a beautiful and fascinating evaluation. Way to go 505, and btw, this integral must not have screamed SOS as it was being taken apart; it too must have been fascinated by the beautiful solution development and enjoyed it.
Really you have an excellent skills to do this. But you forget to write + Constant of integration, because this is an indefinite integral. Thank you for this nice video.
Great! Recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023" You can simply find it!
After your video on the gamma double prime at one it had me thinking Can there be a formula for the nth derivative of gamma at 1 I have put some values in Wolfram and I noticed a two things 1 it's alternating 2 it have gamma constant^n and have zeta at deferent values It will be amazing if it have been derived
@@laincoubert9657 I am already calm, man. And I think you are right about growing up, but I don't think I want to grow up like "you" otherwise I won't be able to understand a simple joke!
Remarkable use of Euler's formula to simplify the integral! But it seems to me like it would be easier starting at 6:00 to just expand e^(i sin x) into real and imaginary parts. It is then easy to find the imaginary part of the product of the three factors, which is what the integral equals, because Re{z/i} = Im{z}.
Such a beautiful evaluation and solution development. It has been a while since I have seen such a beautiful and fascinating evaluation. Way to go 505, and btw, this integral must not have screamed SOS as it was being taken apart; it too must have been fascinated by the beautiful solution development and enjoyed it.
Really you have an excellent skills to do this. But you forget to write + Constant of integration, because this is an indefinite integral. Thank you for this nice video.
Such a clean and artisque solution!
I'm not ashamed to say It doesn't get more fun than that!
Holy. Shit. That was insane!
Great!
Recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023"
You can simply find it!
This is not a qualifying exam
Could this be done without complex numbers
I also would like to know the same
Yes it can be
Awesome 🎉🎉
Thanks!
very well done
At first look I wouldn't have guessed that the answer is even elementary
When in doubt... Euler did it. Somehow.
And if it's not Euler, it's Gauss.
After your video on the gamma double prime at one it had me thinking
Can there be a formula for the nth derivative of gamma at 1
I have put some values in Wolfram and I noticed a two things
1 it's alternating
2 it have gamma constant^n and have zeta at deferent values
It will be amazing if it have been derived
is there anyway without using Euler formula
Complimenti, anch'io avevo usato la Re..,poi mi sono perso..
ok, cool
terribly sorry about that
Yeeeet
plus a constant
Bro are you study on phone this?
Can you integrate e^(arcsin(e^(arccos(e^(arctan(1/(ln(x)))))))dx?
Distracting background talking.
No man
I'm really hurt by the fact that you forgot to write +C.
Like there ain't any more worse way to hurt a integral lover!😢
grow up
@@laincoubert9657 Like really?!
I should say the same to you. If you can't understand a joke, I've nothing to say!
@@rohitashwaKundu91 woah man calm down you look really upset maybe you should grow up
@@laincoubert9657 I am already calm, man. And I think you are right about growing up, but I don't think I want to grow up like "you" otherwise I won't be able to understand a simple joke!
@@rohitashwaKundu91 yea it seems you are very calm