Integrating the inverse tangent – feat. Wurzel-Willi & Linear Leander - Videos

what a dynamic duo

Some constructive criticism:
In the explanation of the expression of cosine in terms of tangent, Linear Leander skipped the step of bringing the cos^2 on the right to the left side, making it harder to follow.

Both for some reason forgot several close parentheses for functions with another function as an argument, and some dxes.

Hi papa, I have two intresting intregals for you
∫ from 0 to ∞ of (x-1)/(√(2^x-1)*log(2^x-1))
∫ from o to π of cosx/(2-sin(2x))
I hope I'll see these get solved in yours video

Could just use the formula for integrals of inverse functions from earlier video.

What is the explanation of the formula

Papa is a shape-shifting lizard with the ability to simultaneously be at two places 🤔😕
P.S- These bad bois overdid the Papa Flammy references :3

Derive the formula for the angular acceleration of both bobs of a double pendulum

Luv what you did with you hair ma boi!! Looks like you finally figured out superposition in the macro world you sly fox

The first math dude forgot the 'dx' man … c'mon!!! … insert heavy metal rift

Проще всего взять интеграл по частям, чем "с умным лицом" разводить смешную бодягу на пустом месте:
int(arctg(x)*dx=x*arctg(x)-int(x*d(arctg(x)=x*arctg(x)-int(x/(1+x^2)*dx, но последний интеграл легко берётся, надо загнать x под знак дифференциала и тогда получим int((1/2)/(x^2+1))*d(x^2+1) откуда и следует результат…Этот пример когда-то в далекие восьмидесятые годы давался в качестве обязательного поступающим в Оксфорд.

Nice one, love the flammy apprentices

there so sloppy in comparison to you papi

Funny that logarithms somehow managed to sneak in by geometry. Scary and exciting.

By the way, the first dude missed a dx so papa, you need to teach them the way of the Flammily, we don't simply miss dx like that!

wowee it is good to see so many math boys in one place

i know the second method only , thanks that u shared me an another way to the problem.

First dude overcomplicates the differentiation process.

2 nd one is the best

Lol the first guy forgot the dx on the integrals

Besser als Wurzel-Sepp.

* Before watching *:
Easy: Int{arctan(x)}dx;

Let tan(u)=x
du=cos^2(x)dx

Int{arctan(x)}dx
=Int{u * sec^2(u)}du

D I
+ u sec^2(u)
– 1 tan(u)
+ 0 -ln|cos(u)| -> Int{tan(u)}du v=cos(u); dv=-sin(u)du; Int{tan(u)}du = -Int{1/v}dv = -ln|v|+c[negligible] = -ln|cos(u)|

Int{arctan(x)}dx
=Int{u * sec^2(u)}du
=u * tan(u)+ln|cos(u)|+c
=x * arctan(x)+ln|1/((1+x^2)^(1/2))|+c

=x * arctan(x)-0.5ln(1+x^2)+c {+ln(1)}

* After watching *:
……….. You're avoiding doing my video idea for THAT ?????? C'mon, Papa Flammable ! ; P

A gud arc boi!

arctan(x) = cos(x)/sin(x)
Let u=sin(x) and u'=cos(x). We have u'/u
Integral of u'/u= ln | u | = ln | sin(x) |

that was really cool, what made it fun for me is that i would have used a completely different way to solve it but this way is a lot simpler

Oh ma boi,where are you ,man ???
I will find you and i will catch you and i will go forword to the camera to make your work !!!

Constructive criticism? Gay

I actually think there was an easier way to get the equality for cos^2. Just say cos^2 = 1/sec^2 and then substitute sec^2 for 1+tan^2.

This is just awful. It is a long, convoluted, sloppy explanation of a simple problem. The problem go way beyond notational issues like not writing dx. The explanation of d/dx arctan(x) is wayyyy too long and with far too many steps. 3/10 only because they eventually solved the problem. Also no spirit or excitement in presentation which, come on, we’re on Daddy’s channel.

To find cos^2(arctan(x)) just draw a right triangle. If tan(theta)=x, then cos(theta)= 1/sqrt(1+x^2) and cos^2(theta) = 1/(1+x^2)…😳

Can you integrate the function (sin^10(x))/(sin^10(x)+cos^10(x))?

first guy looks like male tibees tbh, especially at the end

Was macht ihr denn in Weimar ? :):)

Awesome. Now try integral of ln(x)arctan(x) from 0 to 1 differently than bprp.

dude, what hair fertilizer do you have?

Homeboy resurrected Newton to help with solve this integral

Back to my real analysis textbook. Turns out I've forgotten how to integrate arctan

ma boi papa flammy has dissapeared and has been replaced by 2 strange aliens , one is bald and the other is papa leibniz but with yellow hair, i will find you ma boi wherever you are and i will feed you with some ez integrals

#Yay

WhEn tHE iNtEgrAL iS cOOl buT He ForGOt dX LiKE 3 TiMES

"And because we have no idea how to integrate this, we might as will differentiate this"

LMFAO

Can you please tell me how to integrate legs w.r.t hands

That’s a really cool video, thanks !

I would like to add one thing – they are too quiet imo ._. Also their method was the first i thought about, but i had not seen derivative of arctan before, i just knew this is 1/(x^2 + 1) (mainly becouse of bprp videos :v)

can you do the int(1+1/x)^(1/x)dx?

It's kind of weird that you can figure out the integral of a function whose definition is "give me a tangent and I'll tell you the angle." How do you figure out the general formula for the derivative of an inverse function?

I rate g/10

WHERE IS MY DX?1!!?1!?