I hope you didn't forget your linear algebra for this integral!

[@pangeo8183]

Voldemort's integral

[@lbgstzockt8493]

The Integral which shall not be computed

[@vancedforU]

I read it the same way.

[@dmytryk7887]

For the last problem, the second row has a common factor of ln x, the 3rd and 4th common factors of ln x squared and cubed. These common factors could be taken outside the determinant giving (ln x)^6, etc.

[@saicharanritwikchinni8885]

Revisiting this after such a long time! Nice video..

[@raffaeledavidmammoliti2212]

Nice sleight of hand at 1:19!!

[@BikeArea]

...of shoulder. 😮

[@rainerzufall42]

15:13 Funny, if you think this further... The 12 is just sf(n - 1), if you consider n=4: sf(3) = 3! * 2! * 1! = 3 * 2² * 1³ = 3 * 4 = 12. 265 ~= 6! / e, or better 265 ~= 6! * (1 + e * R) / e = N! * (1/e + R) with N = T_(n-1) = n * (n - 1) / 2 triangle number, R tiny rest. Because you can see that the sum in () is just the partial sum of N! * e^(-1) for t=1 and N! * e^0 for t=0. In general: N! * e^(-t). So the whole area A ~= sf(n - 1) * (T_(n - 1))! * e * (1/e + R - 1/e) = sf(n - 1) * (T_(n - 1))! * e * R with R tiny rest by partial sum.

[@yardenshani586]

After the first operation there is "typo" in indexes you wrote x0^(n-1) instead of x1^(n-1) 5:05 on vid

[@goodplacetostop2973]

15:17

[@VioletSaathoff]

Are there any interesting functions f(y(x)) such that the ODE f(Integral[y dx]) = Integral[f(y) dx] has interesting solutions?

[@akashchowdhury5871]

I would have definitely messed up the last step and take e outside bracket in the final answer

[@UltraMaXAtAXX]

Oh yes, Lagrange interpolation.

[@musicburst2513]

My dumb@ss would've evaluated the entire determinant.