Feynman would be proud. A Wonderful Generalized Integral.

Today we derive a wonderful expression for the integral from 0 to infinity of sin(xt)/te^(-zt). We will make use of the Leibniz Rule for integration / Feynman Integration to get a final expression in terms of the arctan. Enjoy this beauty! =D

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[NPCooking]

Other than that, love ya guys <3

[FF-qorm]

Interchanging the Re() with the integral was bonkers! Never knew you could do that!

[SitremChannel]

Watching you solving integrals really stimulates me to work harder, for some reasons.
Greetings from an Italian physics student

[wuyqrbt]

One of the best Opening ever, actually Grand Opening .... I love you Lovely Papa.
Great video ... Thank you so much 💕

[AlgeArid]

Papa Flammy's slowly losing it in quarantine

[Someone-crcj]

your videos are an emotional roller-coaster for me. i love it.

[williamky]

That’s just the Laplace transformation of a sinc function

[watertruck]

Idk why I’m subscribed to this channel eventhough I haven’t even learnt calculus or integrals yet.

[guillermobarrio]

I would apply the definition of Laplace transform of cosine after deriving with respect to x.

[gabriel]

I love these hard problems with preparation videos because it feels like I'm watching some good Netflix series :D

[tszhanglau]

Oh sht this is amazing!
Looking forward to the next video!

[likestomeasurestuff]

Just curious papa flammy: do you know what your students think of the channel

[TheRandomFool]

Very interesting problem. I tried this before watching the video, and differentiated with respect to z inside the integral instead. I got pi/2 - arctan(z/x), which is equivalent to your answer.

[saranyamitra]

We can also use the division property of Laplace transformation

[gabrieleproietti]

great video but please, next time I need to see the dumpening part on your t-shirt!

[dozzco]

Loved this video!, Also out of curiosity does Papa flammy feed Andrew Dotson His chalk in his basement

[rabiranjanpattanaik]

3:17 Papa what integration technique you mentioned?

[Dakers]

Danke papa. Das ist genug fur heite. Always remember, flammy on top with respect to 0(zero) !!

[euyin]

You could evaluate in the result of the integral obtained in 6:03 directly and that leads to -Re((z + ix)/(z^2 + x^2))

[Abhijitdas]

Loved your take on this integral..Or we can do in other way if I'm not wrong...the whole integral is the Laplace transform of (sinxt/t)....and L inverse of tan inverse (x/z) = Sinxt/t....done