The MVP of Integrals

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Today integrate (x^69-1)/ln(x) from 0 to 1 using the Leibniz Rule for integration aka. Feynman's Technique. Enjoy! =D
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[@jordanfreidel1751]

As a physics boi, I saw the thumbnail and was like “fuck yea we getting into the Feynman shit today”

[@muhammadhabeebullah556]

I said wtf immediately I saw it 😂

[@youssefayman78]

You can get the same result by transforming it into a double integral of 1/xlnx over the region 0 < x < 1, x < y < x^70. You can the flip the order of integration to get the new boundaries 0 < y < 1, y^(1/70) < x < y. By integrating the first integral using a u-sub, the second integral will simplify to an integral from 0 to 1 of ln(70), which is equal to ln(70).

[@FATHERSOFACTUARIALSCIENCE]

Incorrect

[@aweebthatlovesmath4220]

Same integral with power 68 would be better because you actually get 69 lol

[@ethannguyen2754]

Actually you’d get ln(69)

[@pseudolullus]

But no succ'ing it

[@jeequestionsindia]

Then how you'll create thumbnail

[@felipelopes3171]

What helps to see how to apply the Feynman trick is the ln x in the denominator. One of the cases where the Feynman trick simplifies the integrand is when it multiplies it by a factor that helps you integrate.
So, in the case where what's annoying you is something in the denominator one idea is to use the Feynman trick to cancel it out.

[@tomkerruish2982]

So nice to see Papa using the trick that Papa Feynman taught to Papa Leibniz.

[@achrafidou537]

Lol the "don't be a d³/dt³(x->)"
it means "don't be a jerk"

[@mohamedjaballa6811]

Why does it mean that? can you explain pls this is not the first time seeing this and I still got no clue

[@achrafidou537]

@@mohamedjaballa6811
The derivatives of position vector are :
1th:velocity
2th : acceleration
3th :named jerk
And so on
You can see it in matt parker's video

[@achrafidou537]

its called "an unexciting video about distance derivatives"

[@tartaglia4655]

I love how he eventually don't write 70

[@fabboterman]

You killed me with log(succ(69)). Legendary integral

[@rhosymedra6628]

Feynman trick is always fun!

[@xinpingdonohoe3978]

The 69 was clearly an arbitrary number. Also, using e^u=x you it is non elementary. That makes it a clever Feynman, easy enough for me to do in my head. It's fun.

[@CamiKite]

Nice!
I found the same result with another (yet longer) method:
1) Substitute u=log(x) => I=integral (exp(69*u)-1)*exp(u)/u from -inf to 0
2) Expand (exp(69u)-1)/u with taylor serie and switch sum and integral
3) By another substitution you get the gamma function of k on the numerator which is divided by k!, so you find the serie of log(1--69)
OK it's more complicated, but it"s so satisfaying when everything simplify and you recognize a famous serie!

[@neilgerace355]

🎼It's beginning 🎶to look a lot like Christmas 🎵

[@nwa8201]

We can use definite int property intf(x)dx from 0 to a intf(a-x)dx

[@mortify7532]

I did it by noticing that the integrand is the integral from 0 to 69 of x^t with respect to t. After swapping the order of integration, it becomes trivial.

[@danielc.martin1574]

I love leibnitz

[@pseudolullus]

Me too, they make some nice biscuits/crackers!

[@pseudolullus]

Nice one papa

[@kokainum]

Yeah, you should also show that you can change order of derivative over t and integral over x. It's not always true you can do it. Either mention a theorem you're using or prove it.
Here we can do it because for f(x,t)=x^t/ln(x) we have d/d^2 t (f(x,t)) = ln(x) *x^t and it is bounded on sex (0,1)x(t-epsilon(t),t+epsilon(t)) for each t and epsilon taken as small we want for each t>0. It's enough to prove that certain integral in proof is as close to zero as we want. For t=0 the direct proof doesn't work, but it's not needed. Continuity of I_t in 0 is enough.

[@mani_main]

Feynman op

[@memecleave4299]

Where did u get the chalkboard from? Im considering getting one :)

[@decreasing_entropy3003]

6:35 Aren't we supposed to integrate I'(t) instead of I(t)? That should give us I(t) at upper bound-I(t) at lower bound, shouldn't it?

[@PapaFlammy69]

Of course! My bad, small typo, thanks for pointing it out! =)

[@decreasing_entropy3003]

@@PapaFlammy69 Really trivial mistake, not a big deal at all. Keep going!

[@monkerud2108]

You no want beef jerky?

[@lickit77]

nice

[@philippryb5794]

lover bound ;))

[@joshuaalexgeorge]

-68

[@FATHERSOFACTUARIALSCIENCE]

Integrate n times with respect to x, f(x)=x^x^x^x^x^x^x^x^...

[@mr.inhuman7932]

Papa Flammy. It is cold. Why you dressed so lightly?

[@twiddle7125]

You expect us to follow along when you're distracting us with your guns??

[@hcos8139]

Bruh 😂