An extremely captivating double integral

Full solution development for this cool double integral with heavy use of polylogarithms and their properties with full explanation so don't worry if you're not familiar with these concepts. In fact you'll probably be able to brag about all the tricks you'll learn by the end of the video so it's definitely worth the watch.
My complex analysis lectures:
• Complex Analysis Lectures
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[@notfancy2000]

The sign error after the first integral is resolved is cancelled by the sign error with the dilogarithm expansion.

[@maths_505]

Yeah I noticed that while editing but honestly I thought it was so damn funny I left it in as a sort of easter egg 😂😂

[@bingchilling8384]

Thats actually hilarious and amazing

[@ericthegreat7805]

Yo dawg i heard you liked cancelling signs so i made you a sign error that would cancel the sign error

[@unturnedd]

congrats on the ladies view increase 🤣

[@CM63_France]

Hi, "ok, cool" : 4:29 , 6:30 , 7:30 , 10:25 , 11:51 , 13:56 , 17:44 , "terribly sorry about that" : 4:40 , 8:42 , 9:52 , 12:58 .

[@daddy_myers]

ok, cool

[@ethanbartiromo2888]

Wow, I never heard you say “fuck” before

[@SuperSilver316]

I believe it’s the Inversion formula for the Trilogarithm

[@xizar0rg]

I kept expecting you to use the symmetry of the integral for something.

[@vilirbruh3409]

one of few integrals from your videos i actually was able to solve myself, but instead of using dilogarithm integral representation at the beginning, i expanded ln(1+e^(y-x)) into series and after integrating each term collected them into terms with eta function and two polylogarithms, really cool one!

[@maths_505]

Problem with the series expansions for the polylogs here is that they don't converge.

[@Calcprof]

Mathematica quickly gets -(1/2)+PolyLog[3,-(1/E)]+PolyLog[3,-E]+(3 Zeta[3])/2, where PolyLog[k,z] gives the PolyLog function Li_k (z)

[@xleph2525]

Pollywog function? Does it display amphibious behavior and wiggle like a pollywog? Does it traverse the complex plane by hopping like a toad? You still spelled PolyLog wrong, bro.

[@Calcprof]

@@xleph2525 Autocorrect!!

[@redroach401]

@@xleph2525 lol

[@bahiihab-y2r]

sir can you please make an other video about contour integration but this time solving integrals involving the arctan function because i can't really understand the branch cuts in this type of integral i am waitinig for your answer best teacher ever 🥰🥰

[@maths_505]

Aight, lemme find some

[@worldnotworld]

"OK Cool" should be your nickname

[@kingzenoiii]

double trouble integral 😂😂

[@orionspur]

I'll be a lady every other Thursday if that helps.

[@giuseppemalaguti435]

A me risulta I=-1/2+(3/2)ζ(3)+2Σ((-1)^k)coshk/k^3...ma la serie non converge,boh

[@cadmio9413]

19:16 can you make a video where we can see from where 1/3 comes from?, thats the part where I got lost, plis 🙏

[@maths_505]

I'm afraid I'm not qualified enough yet😭

[@ankushparcha5722]

👏✨Well done !!✨👏 And ❤️Thanks! ❤️ for sharing

[@xinpingdonohoe3978]

I like seeing someone else devote a lot of time to considering which letter to make the substitution. Normally I don't use μ, λ or L in case they're mistaken as some kind of Lebesgue measure thing.

[@tamasbarath7501]

At 3:03 shouldn't I= -½ MINUS the double integral?

[@MrWael1970]

Thank you for this innovative solution.

[@zetruxd]

What do you use to write everything?

[@ericthegreat7805]

Can you pls teach the polylogarithm reflection formula derivation? 😂

[@neilgerace355]

19:16 :)

[@hedu5303]

Can you make a crash course about calcalus for people who havent the basics to follow you

[@noobymaster6980]

Interesting integral with solution that includes a coefficient of 4,5 when

[@maths_505]

Yo what are those strange symbols?? I see them on my keyboard as I'm typing and it feels like I remember them from a past life but....what do they mean???

[@petterituovinem8412]

28th

[@roshanmadhav8876]

Didn’t you do this one but It goes to infinity instead of 1 ?

[@maths_505]

Nope...not with infinity.

[@vitorbordini5246]

Why 4 and a half ladies? What is a half lady?

[@gold6836]

Half a lady is a lady cut in half?

[@xleph2525]

That's the DiLady function evaluated at "Terribly sorry about that." Works like a charm out on dates

[@gaminfish]

second

[@maths_505]

Third