UK Integration Bee 2024 #17

[@reaperskyfall6691]

Merry Christmas 🎁🎄 everyone across the globe 🌎🌍

[@owlsmath]

Hi Skyfall. Merry Christmas to you too! 🎄🎅

[@adandap]

Merry Christmas Mr Feynman

[@owlsmath]

Merry Christmas to you Mr adandap!!

[@doronezri1043]

Excellent video 👏👏👏 Instead of Feynman's you can use a fundamental property of Laplace Transform - multiplication with 1/x^2 corresponds to double integration in S domain🍻

[@owlsmath]

Great!!! I like that way better just because it avoids some of the hassle with Feynman. I think you just created another video for me 😆😀

[@slavinojunepri7648]

Excellent

[@owlsmath]

Thanks!

[@ruud9767]

A tough one!

[@owlsmath]

Yeah! Takes some extra effort to apply Feynman twice!

[@Samir-zb3xk]

I parameterized it as I(a) = (0 to ∞) ∫ [ e^(-(a+1)x) - e^(-x) + axe^(-x) ] / x^2 dx; differentiating with respect to 'a' yields a Frullani integral giving I'(a) = ln(a+1), and then using I(0) = 0, integrating back gives I(23) = 24ln(24) - 23

[@owlsmath]

That's really nice! I didn't think of Frullani integral for this. 👍👍👍

[@Samir-zb3xk]

@owlsmath Yea sometimes when doing Feynman integration, placing the parameter in more than one spot can make things nicer Btw Merry Christmas

[@owlsmath]

@@Samir-zb3xk Merry Christmas! And thanks for the idea! :)