2 Awesome Integrals 1 Video [ ln^2(x)/(x^2+1) and ln(x)/(x^2+1) from 0 to infinity ]

[@quahntasy]

I was studying complex analysis today, and you uploaded another one of your miracles. And manliest opening ever.

[@FGj-xj7rd]

One of the manliest openings ever.

[@user-lu6yg3vk9z]

Flammable Maths can u solve this integral of inversetanget(1/(x'(2)-x-1) going from 0 to 1. x'(2)= rasied to the second.

[@ryanmuller9497]

Not sure if I'm missing a running joke but, on the off chance that I'm not, I figure it's worth mentioning that the 'g' in "elegant" is the same as in "goat" or "green", not "gentlemen" or "generic" (as far as I can tell, "elegant" is the word you were going for several times when describing some of the results at the end). Anyway, that aside, great video as usual.

[@anegativecoconut4940]

Don't give me Pi, give me Poland.

[@Ensivion]

always great to get a refresher on these integral, will help out with qualifiers.

[@user-wu8yq1rb9t]

Great Papa, Great! I just learned and enjoyed. Thank you so much Papa 💗

[@PapaFlammy69]

[@soldenstoll8495]

Those are some hot integral signs 🤩

[@starship1128]

Tysm as a University of Michigan student taking Physics 351 doing Homework 9 problem 6.

[@The_Professor_S_]

Another great video Papa!

[@tatjanagobold2810]

Please support Papa Flammy on Patreon! He really need some chalk and new towels :'(

[@funkycude57]

Papa flammys random oiaaaaa

[@parthpawar7837]

Complex analysis :( bounces over my head

[@absolutelymath3399]

FLAMMY=BEST

[@Rundas69420]

30 seconds in and I'm already half dead because of laughter.👌

[@restitutororbis964]

I missed those fucking amazing intros :D

[@JeonJungkook-zn8kk]

Hello Papa Flammy, you're great!!! 😢 I'm not good at maths but I hope I'll get as fantastic as you in my field 😀 Lots of love!

[@kittenhero568]

it took me like 10 seconds before i started laughing at the shirt

[@alexkhortov7893]

wi rielli nied to hit sat poland

[@slavinojunepri7648]

We see you, funny German mathematician 😂

[@rybaplcaki7267]

That opening

[@yusherry3]

Thank you very much!! You save my homework!!! :p

[@h4c_18]

π=0 xD. Nice joking around :)

[@mayankvats926]

That flammable handstand tho😂

[@luisramrod9121]

Your videos get funnier 😂😂😂👍😀😆

[@polychromaa]

I solved both of these integrals using real methods!

[@EmissaryOfSmeagol]

16:41 "ele-JANT"

[@EmissaryOfSmeagol]

lol just being a troll

[@MrJdcirbo]

I need that shirt in my life

[@NeoxX317]

The title reminds me of « 2 girls 1 cup »...

[@treyforest2466]

German Man Advocates for Violence Against Poles, Falls on His Face

[@benjaminbrat3922]

What about the half-circles of radii R and epsilon? They approach 0 when you take the limits but is it that obvious?

[@user-jn4qk3qi4g]

Great vid! Quick question, at the end you write the Real part of the contour integral is pi^3/8, this isn’t technically true right? Earlier you found that the real part was -pi^3/4, and only through algebraic manipulation we got to pi^3/8=I. Anyhow, love the videos, please keep them coming! :)

[@lukandrate9866]

I tried to evaluate this integral without complex analysis and stopped trying to evaluate int[0, π](ln²(sin x)dx)

[@weird407]

I really struggle with this part where the contour "arcs" are zero. In what video is this explained best? Or what source should I read, the only thing I can imagine is trying to draw a hemicircle with ends at +- infinity which would create a flat line. But formally how is this proven?

[@user-jn4qk3qi4g]

I know this is a very late reply, but you can research: - Jordan’s Lemma - the ML Inequality - The triangle inequality These are all methods that can prove that in special cases like this, the arcs approach zero as R and epsilon approach infinity and 0 respectively.

[@Videohead-eq5cy]

uwu what's this??? An integwation to infwinitieeee??? :3

[@SteamPunkLV]

cool vid, sadly I have no idea whats going on xdxd where would you recommend me to learn complex analysis, and what sort of mathematical background do I need (calc 3 or...?)

[@bouteilledargile]

you need to be comfortable with multivariable calculus and then look up the nptel lectures on complex analysis on youtube. that's how im learning it

[@G0r013]

But Log(z) is not analytic on the negative real axis, I think you should have used another branch

[@atrimandal4324]

0:24- Don't die 😕

[@PeterBaumgart1a]

Jens, good work! And enjoyable to watch too, despite of (or maybe because of?) all the profanity you like to slip in... Anyway, a little language hint, and hope you take it well: ELEGANT is pronounced like it is in German, just with the accent shifted to the first syllable, i.e. specifically NOT "eledschant"... And CHALK is pronounced "tschok" in germanized spelling, i.e. with a "silent" L. (You are welcome... No charge :-)

[@dmitryigorevitch7347]

Hi Jens, it's a great work you are doing here. I accidentally stumbled upon your channel trying to solve me own problem similar to this. But I still fail. Maybe you would try to solve it? It's double integral with parameter k, I think it cannot be solved completely, but maybe it can be simplified to one-dimensional one. integral_(-inf)^(inf) integral_(-inf)^(inf) ln^2(1 + k * (x - y)^2) / ((1 + x^2) * (1 + y^2)) dx dy

[@dagatho]

My favorite arcade games are "Punch a Nazi" and "Whack-a-Pole"

[@dagatho]

I don't like "Handstand For 2 Seconds" though because it's 2 difficult 4 me

[@hoodedR]

Btw... The Euler experience thingy... Substituting x-->1/x gives it pretty much directly..

[@hoodedR]

@@PapaFlammy69 oh...😅

[@linuskelsey8295]

generalise for ln^2(x)/x^n+1

[@polychromaa]

You can do this by finding the integral of x^m/(x^n+1) and differentiating with respect to m twice

[@nicbajito]

I laught so hard when you said π=0 😂cuz 0≠3 tho ! Haha nice try

[@michaelempeigne3519]

how to integrate int(from 0 to inf ) [ (ln x) dx / sqrt ( x + 1) ]

[@MA-bm9jz]

Wouldn't it be easier to use x=1/u substitution? And the integral would become ln(1/u)/(u^2+1) du and the boundaries would stay the same and then just add both integrals since they are both from 0 to infinity

[@MA-bm9jz]

@@PapaFlammy69 yeah sorry I thought you did both with complex

[@georgecooper7389]

Coolio

[@Symiatos]

Is it normal that you said before in the video that the integral over the contour c is equal to negative pi cubed over 4 and then at the end said that this is now equal to pi cubed over 8... I guess it was the hidden proof that pi=0 lmao ( 15:19 )

[@assafabram9649]

At 5:40 shouldn’t it be +iπ²/8?

[@boium.]

Yes, he made a mistake there, but on the next frame he puts the i on the bottom of the fracition again so then the minus sign should be there. So there is no continuing error.

[@MrRyanroberson1]

Shouldn't there be ways to solve real integrals without complex analysis? Or have I been trying in vein all these weeks...

[@polychromaa]

I solved these integrals using real methods. It’s possible, but the integral of ln^2(x)/(x^2+1) across the positive real numbers is a hellhole imo

[@andreamonteroso8586]

hahahahahahaha

[@46pi26]

"Many ff-v-f-views... they said"

[@hoodedR]

Flammy: yo fat mama Me: No u😤

[@Riiisuu]

I tried to understand but I can’t I am sorry.

[@surjeetsingh1729iitk]

Good work man

[@themeeman]

Why do you use weird variable names in the thumbnails

[@themeeman]

This is serious math, no fun allowed

[@いじめとの戦い将棋毎日1900]

字が汚ない

[@gakpo_era]

First!