From 8:07 you can recognize it as very similar to a series for tanh that immediately leads to the result, though it's not a genuine huge shortcut as it's obscure and proven with residue theorem.
I love it when you take the 9maginary part of a ρntegral (yes I know the symbol is supposed to be an S for infinitesimal summation, the joke doesn't translate perfectly)
That was one fun ride, once again! ❤ I immediately took note when you lost that pi from the digamma reflection but wasn't quick enough with commenting before you recovered it. 😂
Hey, I was wondering what resources you used to get this good at solving integrals? I'm trying to get better at it, outside from the basic ones you learn at school/uni. Are there any documents/books you recommend with some more 'advanced' integrals? Definitely not ready for the integrals you solve in your videos but I love watching them and would like to be able to solve them one day! Thanks for the videos btw, I've been binge watching them a lot recently 😅
This integrand can be turned into sin(2x)/sinh(2x), at least from trig identities, make a sub 2x goes to x, the integration limits don’t change, and then perhaps you could try a rectangular contour?
I've just had my first math analysis class recently and i got extremely disappointed, they write sinhx and coshx as shx and chx:( Albeit the latter one can be pronounced like 'cheeks' which is fitting since I'll be clapping some soon
I have been watching your videos for quite some time and honestly some of the stuff goes above my head. Can you give me an idea of what chapters/topics/concepts I need beforehand to understand almost every single one of your video? For starters, I have already completed Calculus I (Limits and Differentiation) and Calculus II (Integration). What more do I need to do?
So, there I was looking at the comments to see if someone else had pointed out the transcription error at @14:30, when you corrected it at @15:46. Okay, cool.
Hi, I'm starting my first year of studying maths at university, but i would really love to learn more about these types of functions that are featured in your videos (i.e. the gamma, beta and digamma function). Do you have any recommendations for the best resources to start learning about these concepts? Thank you :)
I am looking for the solution to the following integral: ∫ [from 0 to ∞] cos(ln(x)) * sin(x) * ln(x) dx ? Any analytical or numerical approaches are welcome. Thank you in advance!
kinda silly to replace the imaginary part of a reciprocal with a real reciprocal, and then turning around and writing this as (1/2i) times the original complex minus its conjugate. That's just literally what the imaginary part of a number is, you just did a little walk down the road and didn't even go back in a different route, really
From 8:07 you can recognize it as very similar to a series for tanh that immediately leads to the result, though it's not a genuine huge shortcut as it's obscure and proven with residue theorem.
Ok cool never gets old❤
kamaal bhaiya ne kamaal kardiya
I love it when you take the 9maginary part of a ρntegral
(yes I know the symbol is supposed to be an S for infinitesimal summation, the joke doesn't translate perfectly)
Invoqing the taylor series for psi for the sum is pretty cool 😎
That was one fun ride, once again! ❤ I immediately took note when you lost that pi from the digamma reflection but wasn't quick enough with commenting before you recovered it. 😂
Hey, I was wondering what resources you used to get this good at solving integrals? I'm trying to get better at it, outside from the basic ones you learn at school/uni. Are there any documents/books you recommend with some more 'advanced' integrals? Definitely not ready for the integrals you solve in your videos but I love watching them and would like to be able to solve them one day! Thanks for the videos btw, I've been binge watching them a lot recently 😅
I recommend you to keep watching and learning from his video, his video is better than books.
I've heard good things about the book "Advanced Calculus Explored"
Math is indeed awesome when one is able to understand it.
Peak thumbnail
Finally someone who likes history and maths
This integrand can be turned into sin(2x)/sinh(2x), at least from trig identities, make a sub 2x goes to x, the integration limits don’t change, and then perhaps you could try a rectangular contour?
Yo
It's been a while. How you doin' bro?
A similar integral had been done earlier, I = int(sinx/sinhx) which is twice the present integral
I've just had my first math analysis class recently and i got extremely disappointed, they write sinhx and coshx as shx and chx:( Albeit the latter one can be pronounced like 'cheeks' which is fitting since I'll be clapping some soon
No u wont stop lying to yourself
The former one can be pronounced sehxx which is fitting because mathematician don't do sehhx
we say coshinus for cosh
I'm the half of a lady watching, every video!!!! ✌️
I'm 1 of the 3 ladies watching every video!!
I am gentlemen
fellow lady here ❤
we have located 2.5 of the ladies we must find the last one
Left or right half?
I have been watching your videos for quite some time and honestly some of the stuff goes above my head. Can you give me an idea of what chapters/topics/concepts I need beforehand to understand almost every single one of your video?
For starters, I have already completed Calculus I (Limits and Differentiation) and Calculus II (Integration). What more do I need to do?
Excellent 👌
So, there I was looking at the comments to see if someone else had pointed out the transcription error at @14:30, when you corrected it at @15:46. Okay, cool.
Very interesting. Thanks.
what program do u use for these videos?
I forgot the answer but it was some iPad scratchpad app.
Hi, I'm starting my first year of studying maths at university, but i would really love to learn more about these types of functions that are featured in your videos (i.e. the gamma, beta and digamma function). Do you have any recommendations for the best resources to start learning about these concepts?
Thank you :)
It feels like there should be a way to use the cot series directly.
That's interesting
I am looking for the solution to the following integral: ∫ [from 0 to ∞] cos(ln(x)) * sin(x) * ln(x) dx ? Any analytical or numerical approaches are welcome. Thank you in advance!
I now need the hawk tuah integral
8:04: Where did the 2k go?
He's taking the imaginary part, the 2k only belongs to the real part of the expression.
Tbh the only thing I learned was that apparently sinh(x)cosh(x) obeys a double-angle-identity ;)
Yes. Fuck Yes. How about a tan-version?
Why did I read "how about tax evasion" 🗿
why are you able to write the sum bounds as k>=0 instead of saying it goes from k=0 to infinity
@@the.lemon.linguist it's just notation
when you cancel sin cos and x from both sides, you get 1/h² dx from 0 to inf, which is x / h from 0 to inf. and it is ind. thank me later🥺
This integral could be solved with Residues and a rectangular contour...
This clearly equals x/h^2
OOOOK.... COOL.. so...
1/h^2
@@Shawty-fi2sn best comment so far
You forgot to integrate it. 😂
@@Grecks75 😂😂😂
@@Grecks75 x/h^2+C
If only sinh(x)cosh(x) = 1/2(sinh(2x) 😔
Wow
wait, am I the only one that calls it "shine x" ?
maths 505 making brainrot thumbnails now
Your cancellation of the two series is dubious since the series do not absolutely converge, so splitting and cancelling is not so easily permitted.
@@insouciantFox always (almost anyway) fixed using the limit of partial sums and of course we know the series converge due to the digamma function.
Ho fatto come te ...ma mi risulta un coth(-π/2)...boh
Probably made the same kind of mistake as I usually make
kinda silly to replace the imaginary part of a reciprocal with a real reciprocal, and then turning around and writing this as (1/2i) times the original complex minus its conjugate.
That's just literally what the imaginary part of a number is, you just did a little walk down the road and didn't even go back in a different route, really
No.
This integral could be solved with Residues and a rectangular contour...