Integral

[mossy imp]

Is this correct so Far?

[past pier]

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[mossy imp]

Guys help

[crude mist]

@mossy imp state the question clearly

[mossy imp]

Is there any guide for integrals ? I think I did it wrong

[crude mist]

what is the integral sir

i can't read what u said

[mossy imp]

(1+X)Sqrt(1+X)

[crude mist]

$\int (1+x)\sqrt{1+x}dx$

right?

[upper dock]

CoffeyOnExile

[crude mist]

@mossy imp

$\int (1+x)^{\frac{3}{2}}dx$

[upper dock]

CoffeyOnExile

[mossy imp]

Damn that is a good one

[crude mist]

have you tried any substitutions yet?

[mossy imp]

No never

[crude mist]

let's do

[crude mist]

$t = 1+x$ \ $dt/dx = 1$ \ $dx = dt$

[upper dock]

CoffeyOnExile

[mossy imp]

I mean I can substitute X^2 into y for example but that is way over my knowledge what happens there

[crude mist]

$I = \int t^{\frac{3}{2}}dt$

[upper dock]

CoffeyOnExile

[mossy imp]

That's all?

[crude mist]

$\frac{2t^{5/2}}{5}$

$\frac{2}{5} (1+x)^{\frac{5}{2}}$

,w differentiate 5((1+x)^(5/3))/3

[upper dock]

Results provided by WolframAlpha

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Requested by therealcoffey

[crude mist]

uhh what

OHH WAIT

[mossy imp]

Are you a robot ? XD

[crude mist]

,w differentiate (5(1+x)^(5/2))/2

[upper dock]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by therealcoffey

[crude mist]

fjsshdhs7dyd

[mossy imp]

Did you fail?

[upper dock]

CoffeyOnExile

CoffeyOnExile

[crude mist]

,w differentiate (2(1+x)^(5/2))/5

[upper dock]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by therealcoffey

[crude mist]

okay done

@mossy imp did you understand what I did?

[mossy imp]

Thanks for explaining

Yes kinda

But

[crude mist]

tell me what you didn't get

no "kindas"

[mossy imp]

Nono the way you did was perfect for understanding

But wait

I need to go back to my room to show you something

Ohhhhh well I forgot to tell it has (x^2+1)Sqrt(X+1)

@crude mist

Can we solve this with the same method ?

[crude mist]

ohkY

let's see

$\int (x^2+1)\sqrt{x+1} dx$

[upper dock]

CoffeyOnExile

[crude mist]

@mossy imp this right?

man this one seems hard

but i have a trick up my sleeve

what would happen if we substitute sin(A)

[mossy imp]

That's what our teacher did

[crude mist]

or specifically -sin(A)

ehhh let's try some other way shall we

😄

[mossy imp]

Can you go voice chat.??

Or rather nah?

[crude mist]

$\int x^2 \sqrt{1+x} dx +\int \sqrt{x+1} dx$

[upper dock]

CoffeyOnExile

[crude mist]

the one on the right is doable

the left one

[mossy imp]

Yes that's what I did too

[crude mist]

okay let's make some trigonometric identities,

[mossy imp]

I could stream my tablet if you want, that way you would have less to write 🙂

[crude mist]

$\cos(2A) = 2\cos^2(A)-1$

[upper dock]

CoffeyOnExile

[crude mist]

it's fine

[mossy imp]

Well I am a bit shitty in trigonometry

😬

[crude mist]

now

$\sin(2A)= 1- 2\sin^2(a)$

[upper dock]

CoffeyOnExile

[crude mist]

$\pm \sin(A) = \sqrt{\frac{1}{2}(1-\sin(2A))}$

[upper dock]

CoffeyOnExile

[crude mist]

so let's sub uhhhh sin(2A)

so

$x = -\sin(2A)$ \ $dx = -2\cos(2A)dA$

[upper dock]

CoffeyOnExile

[crude mist]

make sense?

[mossy imp]

Um I lost you in the first step

[crude mist]

$\int sin^2(2A)(\pm sin(A))(-2\cos(2A))dA$

[upper dock]

CoffeyOnExile

[crude mist]

this one?

[mossy imp]

Yes

Is that just another function?

[crude mist]

do yk the cos angle formula

[mossy imp]

Or do we still talk about this one

[crude mist]

cos(A+B) = cosAcosB - sinAsinB

[crude mist]

we used thus functions here :3

[mossy imp]

For me that is abracadabra

I don't understand what's happening

[crude mist]

another substitution

[mossy imp]

How do we come from (x^2+1)Sqrt(1+X) to sinus and cosinus 😄

You mean U substituted the upper in the new function?

Nop not even understand what I am even talking about

[crude mist]

oh That

we forgot about the right part

just working with the left 😄

[mossy imp]

Why is the left turned out like this

[crude mist]

because of the cos angle sum identity

(there's obviously a proof for it)

cos(A+B) = CosAcosB - sinAsinB

cos(2A) = cosAcosA - sinAsinA

cos(2A) = cos^2(A) - sin^2(A)

= cos^2(A) - (1-cos^2(A))

= 2cos^2(A)-1

@mossy imp

[mossy imp]

And how does that turn into the left part. As I said I'm really shitty in trigonometry

[crude mist]

we substitute this

into the left

[crude mist]

and get this see

we just plug the values

here

no manipulation

[mossy imp]

AHH I think it's not good to waste your time with me because I can't see it .

The math you do is 100times stronger than I know.

[crude mist]

@mossy imp I've never done integration.

[mossy imp]

Well but if you know sinus and cosinus

Your math is already 100 times stronger

[crude mist]

no.

trigonometry comes before calculus

way before

[mossy imp]

I skipped trigonometry in school

[crude mist]

i suggest you to study trigonometry brother

[mossy imp]

Because they did not explain where come from

[crude mist]

you'll fail calculus without it definitely

[mossy imp]

Can you quick guide me maybe per voice chat I have my examen on Thuesday. Only if you have time, otherwise I need to connect the dots myself with some YouTube tutorials

[crude mist]

i can't vc but i can give u material

how difficult are your tests

[mossy imp]

I think this year will be no fun.

[mossy imp]

We can take 1 cheatpaper with in exam

Do you study as well?

The only part I am feared about is integrals

Do you have a cheatpaper 🤨

[crude mist]

@mossy imp

https://books.google.co.in/books?id=SnvBeodeTDcC&printsec=frontcover#v=onepage&q&f=false

study this book

[mossy imp]

600 Pages in 4 days?

My attention span leaves really quickly

[crude mist]

no study the trigonometry

it's not much

[mossy imp]

Which site is it

[crude mist]

Google books

buy the book

if you can pirate the pdf

i won't recommend it but yk.

pirating is wrong.

desperate times call for desperate needs

[mossy imp]

Do you mean this pdf ?

[crude mist]

it's the book

iff u can get another copy it's fine

@mossy imp

[mossy imp]

I do never leave the channel as long as you help don't need to ping

[crude mist]

ok sorry

[mossy imp]

What means Pirating

Like writing a program that screenshots scrolls down screenshot and so on

?

Or with Google lense

[crude mist]

it means to unfairly and illegal get books for free.

it's bad.

but.

[mossy imp]

Why hasnt he done it this way around

[crude mist]

uhhhh idk

[mossy imp]

Is this the error?

[wooden lark]

$\frac{d}{dx} \sqrt{1+x}=\frac{1}{2\sqrt{1+x}}$

[upper dock]

Ludwig

[mossy imp]

could you p lease check this?

forget a dx

[wooden lark]

$\int 2\sqrt{1+x} dx=\frac{4}{3} \cdot (1+x)^{\frac{3}{2}}+c$

[upper dock]

Ludwig

[mossy imp]

There are still mistakes in

[mossy imp]

@wooden lark

@crude mist

[mossy imp]

+close