2 fascinating integral results you should know for an integration bee 

Could you possibly think about doing a sort of “study guide” or course for integration bees?

Aaaaah I was waiting for that ! Thank you for it.

"integration with respect to u" With respect to you, sir

Axel Arno, oui monsieur ! Excellent pronunciation by the way and really nice solving ;)

I did this quite differently. I split each integral at x=1 and used power series near zero for one piece or near infinity for the other piece, approaching x=1 in a limit. This expressed the integrals as series of the sequence s that look like (p+n)⁻¹ where p=s/k. At that point, it's just a matter of recognizing that what you get are the Eisenstein series for cotangent or cosecant, depending on if the terms alternate. You get a (-1)⁻ⁿ in the sequence for the first integral, which gives cosecant.

Thanks for the video, very cool integrals These integrals converge for 0

Nice to have these Mellin transforms handy!

This is truly gorgeous! I am falling in love with the plethora that the Gamma, Beta and Digamma functions have to offer...

- I think that i wrote it wrong- B(v,y)=integral(2xcosx^v-1 sinx^y-1) from 0 to pie by tow, if the limits of integration were something else, what do we do?

Amazing Video 😊❤ I love mathematics like you so can I talk to you please ?

A challenge for you 😊: Compute limit n->infinity of (Integral from 0 to 1 of 1/(1+x^n) dx)^n

Hey could you do a vedio or even a series on integrals of JEE mains or Aadvanced - i would ve intesting and informative for students

It is very interesting solution. Thank you

What is known about s and k in both these above? Also, PV is due to the singularity at 1, isn't it?

I have only looked at the first integral so far. May be I have missed something. But immediately my first thought was that the integral could only exist for k sufficiently larger than s-1. Yet this does not figure anywhere in the solution. What am I missing?

Would be good for iit adv also

Il primo è ovvio,basta porre x^k=t...si ottiene β,e poi con le proprietà di Γ,si arriva al risultato...il 2 è meno ovvio,almeno per me

If i share this to my friends they call me math nerd

Axel Arno le boss !!!

I lose a small part of my soul every time a /gamma is cancelled out from the final solution