A very interesting integral: int (0,infty) (sin(x)cos(x))/(sinh(x)cosh(x))

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A beautiful integral solved using some of my favorite tools.

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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. 😂

Grecks

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.

Shindashi

Invoqing the taylor series for psi for the sum is pretty cool 😎

Akhulud

Math is indeed awesome when one is able to understand it.

mcalkis

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)

MooImABunny

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 😅

gustdewit

A similar integral had been done earlier, I = int(sinx/sinhx) which is twice the present integral

daniello

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?

SuperSilver

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?

deviLOfHELLsKitchen

I'm the half of a lady watching, every video!!!! ✌️

maxmoedough

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.

jimschneider

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 :)

BigTonyPersonal

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

Spiderp-pl

It feels like there should be a way to use the cot series directly.

waarschijn

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🥺

EobardUchihaThawne

This integral could be solved with Residues and a rectangular contour...

vascomanteigas

Tbh the only thing I learned was that apparently sinh(x)cosh(x) obeys a double-angle-identity ;)

naturallyinterested

why are you able to write the sum bounds as k>=0 instead of saying it goes from k=0 to infinity

lemon.linguist

what program do u use for these videos?

chiva

Yes. Fuck Yes. How about a tan-version?

F-S.

A very interesting integral: int (0,infty) (sin(x)cos(x))/(sinh(x)cosh(x))

A very interesting integral: int (0,infty) (sin(x)cos(x))/(sinh(x)cosh(x))

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