I Was AMAZED By This Integral's Secret...

Hope everyone enjoyed! Shorter more quick integral today but stil a nice, fun, problem - please comment with any questions or suggestions for new topics, and as always, subscribe to stay updated.
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Comment answers to the challenge down below.
‪@blackpenredpen‬ ... I challenge you!
Thanks so much for all the recent support - hitting 4k subscribers has been amazing and so please keep sharing and interacting so I can make even more content!
Thanks again for all the recent support and please keep sharing and interacting!!
#maths #mathematics #integrals #entrance #university #Oxford #Cambridge #JEE #problemsolving #taylor #maclaurin #gaussian #gauss #statistics #whoknew #fascinating #functions #euler #funproblems #proofs #functions #physics #sums #series #limits #whiteboard #math505 #blackpenredpen #integral #trig #trigonometry

[@netanelkomm5636]

Would love to see a video of you deriving the gausssian integral result (I love your voice)

[@OscgrMaths]

@@netanelkomm5636 Maybe I'll do one soon then! Thanks so much.

[@mathletics6287]

Man, that was a crazy ride. I got so much of that adrenaline pumping at every step. Thank you for this masterpiece.

[@OscgrMaths]

@@mathletics6287 You're welcome... definitely a fun and exciting integral!!

[@MattiVäätäjä]

I noticed that this integral from 0 to infinity gives e*sqrt(pi), double from e! Fascinating

[@OscgrMaths]

@@MattiVäätäjä That's amazing thanks so much for sharing that!

[@Mephisto707]

This same function integrated from 0 to e gives the same answer!

[@OscgrMaths]

Amazing!!

[@EvergrowingInfinity]

What an elegant solution!

[@OscgrMaths]

@@EvergrowingInfinity Thank you! I'm so glad you enjoyed.

[@lubiemuze6368]

Ah yes, next golden math youtuber on my main page on youtube

[@FPSIreland2]

That was beautiful. What an answer!

[@OscgrMaths]

@FPSIreland2 It's such a lovely question!

[@Cooososoo]

Would love to watch more integrals thanks buddy❤

[@OscgrMaths]

@@Cooososoo No problem! Glad you enjoyed ❤️

[@jasimmathsandphysics]

Wow amazing

[@OscgrMaths]

@@jasimmathsandphysics Thank you!

[@noteventrying27]

nice video, truly an amazing integral!

[@OscgrMaths]

Thank you! I'm glad you agree, I thought so too.

[@wjeksababakqabzzhzaab873]

please can you do some more BMO problems

[@OscgrMaths]

@@wjeksababakqabzzhzaab873 Yes! Thanks so much for the comment.

[@noteventrying27]

@@OscgrMaths what is bmo lol

[@OscgrMaths]

@@noteventrying27 It's the British Mathematical Olympiad!

[@beuhs545]

it sorts out very nicely if you do the substitution t=1-lnx and can be done in just a couple of steps. Awesome integral.

[@lotaniq4449]

Will you continue your series on Bernoulli numbers or is it finished? I really love the videos about it from you.

[@OscgrMaths]

@@lotaniq4449 I have one more that should be coming along soon to finish it which will be a bit longer where we finally look at their relationship to the zeta function! Not sure when it'll be up but definitely soon.

[@jcfgykjtdk]

Nice

[@OscgrMaths]

Thanks!

[@adityadeodhar8819]

L N not lin!!!

[@lagomoof]

Different places learn different ways to pronounce it. It's like the linear standard form being y = mx+c in some places but y = mx+b in others. Some say l(i)n, some say lawn, some say _logarithmus naturalis_ and you and I say L.N. with slight emphasis on the N. At least, I assume we have the same emphasis. The other emphasis is traditionally a girl's name, after all, but maybe that's common in some places too.

[@k_wl]

i was thinking of approaching it a different way cuz i didnt wanna end up with the gaussian integral even if i know the value lol, nice solution

[@OscgrMaths]

@@k_wl Thanks! Let me know if you find another approach.

[@Flixs_Shots]

i have absoluetely no clue what is going on but i cant stop watching these videos, how can i learn this and where should i start?

[@OscgrMaths]

Wow!! I love this comment because this is how I was inspired to learn maths too... you should watch the series on calculus from the KZbin channel '3blue1brown'! Then once you've got the basics, come back to the channel and ask any questions you might have. Blackpenredpen also has some great content for once you understand this more! Best of luck and always feel free to ask questions!!

[@gonzalomorenohirata]

amazzzzzing!!

[@mathevengers1131]

I did this integral in my head by u substitution in the first step itself. No need to write it as e^ln(x).

[@OscgrMaths]

@@mathevengers1131 Absolutely right, just wanted to make the substitution easier to follow in the video. Hope you enjoyed anyway!

[@Vengemann]

That was a cool integral ngl

[@OscgrMaths]

Thank you!

[@dean532]

I’m curious to ask, do you happen to teach in college or university?

[@toony966]

Do you have any calculus book recommendations?

[@angadbains7125]

Just curious, did you go to uni / are you at uni, and what did you study. Great video btw, I love watching your channel to learn maths since I am currently doing my A Levels!

[@JohnBerry-q1h]

I get the feeling that, one day, the Fundamental Theorem of Calculus might be shown to have an exception, so, for that reason, some people endlessly pose and attempt these insane integrals, hoping to demonstrate an exception to the Theorem.