Bernoulli's integral has a few tricky things going on

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[@jackkalver4644]

I have to admit, the sum is a good form as it converges very quickly.

[@user-pf6jl6mu1n]

Riemann agrees... 😂

[@adandap]

Such a beautiful result. 😊 The same calculation for x^(-x) gives a very nice symmetric result of Sum[1/n^n] (n=1, 2... )

[@owl3math]

Yes this one is nice! :)

[@iqtrainer]

This one is called Sophomore's dream. Dr. PK evaluated this a few months ago

[@owl3math]

Oh nice. I didn’t know that name for it

[@iqtrainer]

@@owl3math You and Dr PK should collab on an integral. You two are two math youtubers posting challenging integrals I know

[@owl3math]

@@iqtrainer I like Dr PK!

[@panyachunnanonda6274]

Very nice; problem+ solution.

[@owl3math]

Hi Panya. And thanks! 🙏😀

[@alvargd6771]

u can shift to -\sum_{n=1}^\infty\frac{(-1)^n}{n^n} to make it nicer

[@PaoloACostantino]

by reiiterate integration by parts

[@uselesscommon7761]

Pi/4 moment

[@isavenewspapers8890]

I got a notification for this video while writing the name "Bernoulli".

[@owl3math]

oooooh weird

[@felipefred1279]

I thought that you would use Laplace transform again hahaha

[@owl3math]

ha! I do like to use that quite a bit :)

[@Reetdawn]

SIMPLE ANSWER: X^X-1/X-1

[@owl3math]

is that supposed to be x+1? Power rule :)