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

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Merch :v – https://teespring.com/de/stores/papaflammy

Those two bad bois sadly have no YT channel but still! Enjoy the show and show some love to those brave fellas! =D

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1. 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.

2. 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

3. 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.

4. 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!

5. * 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

6. 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.

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 ma boi papa flammy has dissapeared and has been replaced by 2 strange aliens , one is bald and the other is papa leibniz but with yellow hair, i will find you ma boi wherever you are and i will feed you with some ez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

8. 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)

9. 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?