A beautiful iterated integral

My complex analysis lectures:
• Complex Analysis Lectures
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[@maths_505]

The log(sin(x)) series: kzbin.info/www/bejne/o6Kzhal7ga-Dg5I If you like the videos and want to support the channel: www.patreon.com/Maths505

[@abdulllllahhh]

Integral so beautiful I couldn’t even edge to this, I exploded immediately!!! Clean up on aisle MY PANTS 😂😂😂😂

[@maths_505]

😂😂😂

[@two697]

Why are youtube users so late to every trend

[@xantrixx]

💀

[@eu7059]

My boy π²/4*ln2 was truly the main character of the show

[@maths_505]

Yeah it got butchered at the beginning but refused to go down 😂 Them: why don't you give up! Me: cuz he didn't 🔥

[@adalbert_9104]

4:45 Why does the integral from 0 to π/2 of log(sin (z)) evaluate to (-π/2 * log(2)) ? Is it something really obvious that I'm missing ? Or is it just kind of a "well known" integral ? Edit : I tried to compute the integral using king's property and found that it indeed gave me -pi/2*log2

[@kucckumelon2837]

Wow knowing the Euler's log trig functions really helped in the solution development. Btw I'm really liking that bright yellow colour at the end. Keep up the good work!

[@ankushparcha5722]

🙏❤️Thank you very much❤️🙏 for choosing my problem and ✨🤍your video solution✨🤍 is 👏detailed👏 and 💘nice as always💘 💖Best wishes💖 for your 💛💚upcoming videos 💛💚

[@felipealonsoobandolopez9957]

heyy,,.... can you help me to proof that Ci(x)= γ+ln(x)+int zero to infiniti of (cost-1)/t ?? pleaseee kjkjkjkjk

[@Mr_Mundee]

solve this integral: int 0-->1 tan(lnx)dx. two techniques: complex version of tangent and the fourier series for ln(cos)

[@leroyzack265]

As always you propose us good stuff. The previous differential equation you did was such a fonction where y could not be written in terms of X. And the tetration of the matrices you proposed was equally a nice exercise of reflection. I'm sick when you don't release a video because your videos are my favourite content. Keep producing such wonderful stuffs.

[@maths_505]

Thanks mate

[@satyam-isical]

Congrats for 50k Soon silver play⚡👍👍

[@cosmicvoidtree]

Another way to write the result is 7/8*Z(3)+3/2*Z(2)*ln2 Edit: Z is the zeta function

[@ugwunnadiobioma123]

How do I integrate √(x). with limits from -5 to -1.

[@satyam-isical]

I'm dead 😦

[@srinjansingharoy202]

my condolences

[@Unidentifying]

Bro you are hilarious and a genius

[@manstuckinabox3679]

10:00 wouldn't king's property be helpful on the right most integral? edit: Oh LOL you did the exact same thing. Great vid as always! I feel like I'm missing alot since I don't have much time to enjoy these insane videos, thank you as always for your awesome work!

[@我孫子あ]

So unique and beautiful integral!!

[@jieyuenlee1758]

16:06 why the surrive term not pi²/2 log2

[@maths_505]

I fixed that towards the end of the video 😂

[@baskarannadar2138]

your expansion of log(sin x) to -log2 - sigma at 11:41 is not clear. ???

[@maths_505]

See the pinned comment

[@baskarannadar2138]

🙏@@maths_505

[@juancarloscenteno3871]

Which software do you use for writing the equations?

[@sophiophile]

Can someone tell me thebnamw od rhe identity in step 2?

[@aidenmcdonald5605]

this inspired me to evaluate ∫∫ ln(tan(x)+tan(y))dxdy took an hour and evaluates to the same answer!

[@maths_505]

Fascinating

[@maddog5597]

Please, please, for everyone’s sake - USE A SCRIPT!!!

[@maths_505]

What happened this time 😂??

[@SuperSilver316]

I’m happy that I can do the problems in the thumbnail and then come back to answer have it be right!

[@maths_505]

Mashallah

[@maths_505]

I'm proud of you bro🔥

[@MrWael1970]

Thank you for your featured effort.

[@mcalkis5771]

How do you come up with the integrals you solve?

[@maths_505]

This one's from the Romanian mathematical magazine

[@mathalysisworld]

From RMM

[@valdemardomingos1275]

How do you expand log(sin(x)), in minute 11:41?

[@maths_505]

See the pinned comment

[@chessclips8381]

Great content!. What software do yo use?

[@chessclips8381]

?