A beautiful result in calculus: Solution using complex analysis ( Integral cos(x)/(x^2+1) )

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Let us compute this AMAZING result in modern analysis using everyone's favourite integrationboi: Contour integration. Papa Cauchy would be proud :)

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[kilian]

I remember watching this for the first time and not understanding anything. Now I’m finally studying complex analysis and I understand everything :)

[alephnone]

I love how the humor and commentary is integrated (no pun intended) as you walk us through the solution. Well done!

[damiandassen]

Could you make a video of integrating x dx in the most hardest and inefficient way possible?

[TheMauror]

A similar one was on my complex analysis final exam, it asked to find the integral from -inf to inf of x*sin(x)/x^2+1, surprisingly the result is the same, pi/e. Amazing!!! But to show that Gamma tends to zero as R tends to inf I just used Jordan's Lemma hahahaha

[MooshPeriwinkle]

real boi + curvy boi = real curvy boi ;)

[dominikstepien]

Do more complex analysis videos, please! They are fun to watch and there is not that much of them on youtube.

[jameswilson]

Very nice video. I like that you get to the point quickly in your videos. By the way, the integral where you write the limits as R to -R is a poor notation in my opinion because the integral depends on the path. In particular, if you take a (continuous) path from R to -R that crosses the imaginary axis somewhere between i and -i, then the value of the integral is -pi/e instead of 0 (for those who don't know).

[remlatzargonix]

I think your videos are great!....You have enormous enthusiasm and a great sense of humour....keep up the great work.

[ГЕОРГИЕДРЕВ-юр]

"And now we need to take a look for the poles...."
- Someone's FLAMMABLE grandpa,
September 1st, 1939.

[RaymondRossell]

You're freaking hilarious!! (And brilliant too)

[ruskolnikov]

That first contour integral sign you drew. Beautiful.

[prateeksingh]

You explained it excellently. Even a dumb like me got everything except, why did we replace cosx by e^ix🤔🤔

[housamkak]

Hey, i don't know how to integrate on a complex plane and stuff uve done and contour stuff, so please can u make a video explaining these things.

[lionelinx]

I love ur complex analysis videos the best

[amineelfardi]

I'm not familiar with complex analysis but I still enjoy this =)

[aniketeuler]

He made complex analysis so simple that my mind is now being complex at everything

[lucascruz]

Yes, thanks to your videos, I (a freshman) got to solve this 😎

[soliscrown]

I've thoroughly enjoyed this three part series. What's on the horizon for Flammable Maths?

[michelkhoury]

Nice and correct solution... I solved it by the same way... I love very much complex analysis

[xerxes]

Thank you sooo much. This was beautiful.