วีดีโอ

Is this for undergraduate course??

good job

Pa

No, n=Log(1+√(5)/2)/Log(3/2)

i regretted skipping

I think you forgot a 1/4 factor after the u sub from the dx term

I did it the lame way with three subs: u=sinx, v=sqrt(2)*u, w=-lnv. Great video

I had a friend once his name will not be announced but for the sake of the story I’ll call him Phil, basically Phil was a friend of mine who I met while in grad school one night when I was at this bar getting wasted because my fiancé (total whore) cheated on me with my professor in gender studies, I still do not see what she saw in the guy he wore massive glasses and had a fat nose looking like the irl incognito glasses you could buy at dollar tree. Anyway Phil came up to me like the CIA doing a sting and told me he could help me outta this pickle I had myself in saying he’d seen guys like me all the time and decided it was time to help me anyways I went with him back to his apartment which smelled like mildew and my grandmas fridge but I didn’t pass any judgement. Phil told me he would help me expose the professor my fiancé cheated on me with by going into his laptop and downloading all of his files for dirt on him, the only problem being a dropped the class right after so I’d have to go back and join it again anyways catch you for part two

now this is epic

You wanna see monstrous? I'll show you what I did in the toilet today.

Dammn good bro 🔥

Just my view... all matters become from applying u-substitution to earlier one. 😂😂 By the way always thx dude, to your introducing solving strategies.

What a brilliant method! Transforming the expression into a function! 👍

I put it into desmos, and it didn’t work… the graph looks like y=1{x<1.5} Any idea where I went wrong?

I transformed the single integral into a triple integral switched the order of integration and got the same answer.

Or a theta-substitution: x = 2 tan θ dx = 2 sec^2 θ dθ So I = int from 0 to pi/2 of 2 sec^2 θ ln (2 tan θ) dθ/(4 tan^2 θ + 4) I = int from 0 to pi/2 of ln (2 tan θ)/2 I = int from 0 to pi/2 of ln 2/2 + (ln tan θ)/2 = (pi ln 2)/4 + int from 0 to pi/2 of tan θ int from 0 to pi/2 of tan θ = int from 0 to pi/2 of sin θ - int from 0 to pi/2 of cos θ = 0 I = (pi ln 2)/4

Nice video Ben!

Nice explanation man, I have to prepare a report regarding Mathematical Fallacies, Your video definatly helped a lot

Wow this formula is look so beautiful 😍😍

Futurama theorem video :)

Welcome back! 😊

Welcome back :)

Now do n^^x instead of x^^n

thanks 👍👍

Madhav libnez

can you make a video on the futurama theorem

Now do the same for pentation.

It's really good man, but I can't show this solution to my teacher, because now I'm a first year university student and he won't believe that I understand this.

???? Overall, the approach is beautiful, but (0-1) ln(a/b) = -- ln(a/b) = ln(a/b)^-1 = ln(b/a), or am I missing something?

I was obsessed with this equation ever since I "found" it 10 years ago! Thanks for showing me the proof!

Impressive however the floor function is not positive definite. You must consider the possibility of negative solutions

C U R S E D

Omg this was so helpful! Doing squares nested in circles, so I just started my work at EFGH and went from there. You are a lifesaver, this makes so much sense!

3:36 although numerically correct, I think, because we are equating ratios between similar triangles, the second ratio should be expressed as ab/bc rather than ac/bc (because c is only present in one triangle so that is comparing two sides within one triangle). I really like the geometric proof, having come across it while trying to fathom pentagons.Thanks.

Real nice job.

I really enjoy your integral!

The way you split the sum in two at 6:45 does not work as both terms sums are infinite.

First

why did you substitue x back in as x when you have declared x = -u?

Beautiful

why dont use maclaurin developpement to get the answer quicker?

Good

9:45 thanks for letting me take the screenshot :)

The beta function has so many identities I can barely keep track of them When in doubt, invoke the beta function. It always finds a way to work

I've made it nicer: (ⁿx)' = ⅟ₓ⋅Σⱼⁿ₌⁻₀¹(lnʲ(x)⋅Πₖʲ₌⁺₀¹(ⁿ⁻ᵏx)) Hope It's readable enough!

Wtf injection xd

😂

Hello

What does those signs represent

A College question