Another NICE solution using 2024

[@krisbrandenberger544]

The final answer can also be written as (pi/2024)*csc(pi/2024).

[@owlsmath]

nice! Yep flip the sin over and there it is

[@taranmellacheruvu2504]

Very fun exploration near the end!

[@owlsmath]

Thanks! Yes i really liked that part of this problem :)

[@MikeMagTech]

That ended up being a very interesting and fun problem.

[@owlsmath]

thanks Mike! Worked out much nicer than what I expected originally :)

[@adandap]

The approximation will improve every year!

[@owlsmath]

yes its quite true! 😁

[@mohandoshi153]

This problem and its evaluation could do any elite school integration Bee proud. Great to the see the Gamma function and the Beta Function pop up. Lovely solution development.

[@owlsmath]

Thanks Mohan! Yes really liked this one and the fact that we get both an exact solution and a nice estimate. 👍

[@I_like_smashburgers]

imagine the question just asked for 3dp lol great video btw

[@owlsmath]

Thanks!

[@the.lemon.linguist]

i wonder if there's some generalization for this improper integral for any power n in the integrand 1/(x^n + 1) or if there may even be a generalized antiderivative

[@theelk801]

there most definitely is, you can use the residue theorem to do it

[@owlsmath]

Yes the formula is pi/ (a sin pi/a ). For a > 1

[@koennako2195]

Yeah. I remember watching a Dr. Payam video on this generalization. Cool stuff!

[@krisbrandenberger544]

The final answer can also be written as (pi/2024)*csc(pi/2024).

[@vijaypraneeth2736]

Michael Penn got a video on it, he generalized it.Check it out

[@beaumatthews6411]

Bro Im straight laughing but this is great!

[@owlsmath]

Thanks!