This Integral Will Make Your Day

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#math #brithemathguy #calculus

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

[Hadar]

At least it is not another "let's abuse notation to the point of war crimes and put dx in a random place". :D

[Shivamwastaken]

It is 1 am for me, it might not make my today but i am sure it will make my tomorrow :D

[TelPerson]

Hello! This is very interesting integral and a nice video! But shouldn’t the lower formula at 0:10 be like this:
ln(x^n) = n*ln(x) ?

[Ninja]

We can do a very similar thing with the integral for x^(-x) and we would get the exact same infinite series just without the alternating.

Which is itself pretty neat because
integral x = 0 to 1 of x^(-x)
=
sum n=1 to inf of n^(-n)

[LoulouMaths]

OMG I posted this video on my channel 2 hours before you, what a coïncidence !

[shmuelalexis]

I have been pondering this integral for ions without a solution. Finally you made a video about it

[shahishtahassan]

for those searching for a more basic but bit lenghty method:
take lnx=t then start integrating as a polynomial of t along with sure you calculate nicely)
n there you are! with the same result of the integration...now you just apply the sigma notation and find the approx value as given above

[astroashruff]

this is actually one of the beautiful solution for non elementary function

[joeschmo]

"Fun" integral? I'm going back to watching kitten videos...

[bhargavib]

Very Intresting!These are really good quality videos.

[adityashimoga]

Could you also explore the topic of whether or not 0 is an ‘imaginary number’?

[Nguyễn-jq]

Well trust me (desmos) is also an helper

[marksmith]

I must be in the wrong place. I wanted to see Pumba hissing.
Nice integral btw.

[marquesjr.]

Thanks! Using taylor series trick to solve problems almost always make it more easy :)

[gamemakingkirb]

Nice video, and I think I’ll watch a couple more from you :)

[EyadAmmari]

You differentiated with respect to N. I missed the part where you have to integrate with respect to N back. What did I miss?

[parkerfero]

Do we have an exact value? Or is the approximation of 0.78 all we can find here

[familychannel]

Hello,
I have discovered mathematical formulas that can identify all non-prime numbers, allowing me to deduce all prime numbers. Does this discovery hold any scientific value?

[laxario]

The result isn't π^2/12?
Edit:No, it was not

[elreturner]

Ok cool but now just take the antiderivative of x^x the derivative is pretty simple but tried to do an antiderivative gave up went to wolfram alpha and gave up on understanding it