Can anyone help me with that integral?

[red jolt]

Try
u = x^2 + 4x - 4
u' = 2x + 4
You’d notice 2x + 4 is similar to something in the integral

||When doing this, don’t forget to change the bounds||

[woven copper]

okay wait a min

i think i managed to do it

[red jolt]

Yeah that’s right

[woven copper]

thank you for reminding me what to do

i keep forgetting

what i need to do

when changing variables

[red jolt]

I would say when you look at an integral, see if you are able to do a u-sub. If you can’t, see if you can do partial fractions (which may be obvious), and if those don’t seem to work out, try if integration by parts can work

[vocal dome]

Mhm, you can multiply by 2 and divide by 2

Multiply to get 2x+4 and then sub it in

[red jolt]

Mhm

[woven copper]

Thank you I will take give an extra care for that

[vocal dome]

Bro partial fractions are actual hell though. $\int \frac{1}{x^{5}+1}dx$

[delicate cargo]

axkyn

[red jolt]

(I should’ve say if you have powers under 3, then you can consider partial fractions)

[vocal dome]

The trick is to find a u sub that works and then the deravative and try to see if f(x) contains it

[red jolt]

Powers above 4 are ☹️

Even powers of 3 are annoying

[vocal dome]

Powers above 4 is crazy lmao, lol look at this

,w integral of 1/(x^5+1)dx

[delicate cargo]

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[vocal dome]

[red jolt]

I don’t even know how to do this 😭

[woven copper]

i don't know anything about partial fractions tbh

[red jolt]

😭

[woven copper]

Most likely extracurricular here

[vocal dome]

Just find roots and pray stuff works lmao

[red jolt]

It’s just when you decompose a rational function into a sum

It’s more of an algebra thing

[woven copper]

Or its a higher class thing idk

[red jolt]

But it’s used in calculus to integrate rational functions

[vocal dome]

Do your teachers not have decomposition in calc syllabus

[woven copper]

nah

[vocal dome]

I don’t like it man

[woven copper]

education in turkey is like a chicken driving a car

[vocal dome]

Frisk can I reccomend you another funny integral

To practice u you sub

[woven copper]

That would be cool

[vocal dome]

$\int x^{3} e^{x^{2}} dx$

[red jolt]

So an example

(2x + 6)/(x^2 + 3x + 2)
⇒ (2x + 6)/(x + 2)(x + 1)
⇒ A/(x + 2) + B/(x + 1) = (2x + 6)/(x + 2)(x + 1)

Then you’d multiply both sides by (x + 2)(x + 1), solve for A and B, then integrate each individual term because integration is a linear operation, sooo
∫ (a + b) dx = ∫ (a) dx + ∫ (b) dx

Partial fractions are fun SOMETIMES

[vocal dome]

Brooo

[red jolt]

I love u sub its so satisfying

[delicate cargo]

axkyn

[vocal dome]

There we go

[woven copper]

what the actual fuck

Erm

[vocal dome]

Hint, set u=x^2

[red jolt]

Erm.
u = x^2
du = 3x^2 dx
du/3 = x^2 dx

😭 ?

[vocal dome]

I like u sub not partials

[vocal dome]

???

2x?

[red jolt]

Oh..

[vocal dome]

D/dx(x^2)

?

[woven copper]

nah man i think i will fail my exam tomorrow

i am cooked

[vocal dome]

I would say this is a fair bit harder u sub wise

[red jolt]

Wait wait
I meant u = x^3,so then u' = 3x^2

[red jolt]

Do you have another integral you need help with

[vocal dome]

Yeah it doesn’t work lol

Here let me do the work

Do you want a solve

Or

[woven copper]

for now not

but there can be very after a minute

[woven copper]

i am checking on this rn

[red jolt]

@vocal dome is there an early logarithm

?

Nvm

@vocal dome you can solve it

[woven copper]

theres no hope for me

[vocal dome]

What?

You could evaluate this integral prob

Through ibp

So like

1/2(u times e^u- integral of e^u du)

So 1/2(u times e^u-e^u)+c

[woven copper]

i guess i got it

[vocal dome]

Then just evaluate u=x^2

[red jolt]

∫ (x^3)(e^(x^2)) dx
u = x^2
du = 2x dx
du/2 = xdx
∫ du/2 • ue^u
(1/2) ∫ ue^u du

[red jolt]

Yeah

[vocal dome]

I’ve never seen that manipulation before lmao

[woven copper]

guys what's integral d(cosx)

[vocal dome]

After I’ve substituted I just do that 1/some function

[vocal dome]

What’s d

[woven copper]

Just d

[vocal dome]

Constant?

[red jolt]

d 💔

[woven copper]

is it cosx+ c

[vocal dome]

Idk what d is

[woven copper]

wait lemme take a pic

i guess its a

[red jolt]

I’m assuming d is a constant..

and the integral doesn’t even have dx

[vocal dome]

Maybe it doesn’t understand dx lmao

It should be sin x if this occurs

But obviously it’s wrong 😄

[red jolt]

Wellll the integral of cos(x) is sin(x)

But there’s no sin(x) 💀

[woven copper]

so this should be a non existent thing

[vocal dome]

Wth is this question

Guys you should try $\int \frac{arctan(x)}{1+/frac{1}{x^2}}dx}$

[delicate cargo]

axkyn
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vocal dome]

What

Oh I’m bad

[woven copper]

its from a books first test on integral

[vocal dome]

It’s just integral of atan(x)/(1+(1/x^2)) dx

[woven copper]

it says easy section on it

[vocal dome]

It’s a funny solution

[final lodge]

cosx+c i believe is the answer to this one

[vocal dome]

How?

[final lodge]

idk how to use latex, gimme one sec imma write in ms paint and ss it

[woven copper]

the question above has no dx too (don't mind the language)

[vocal dome]

What is this brooo

Is this like

Differentiating first

And then taking integral

[woven copper]

probably?

[vocal dome]

AHHHHHH

YOU GUYS ARE LEARNING FTCP1

Lmao

[woven copper]

what is that 😭😭

[vocal dome]

Fundamental thereom of calculus part one

[woven copper]

i am fucking Turkish highschooler idk about english terms so much

[final lodge]

https://en.wikipedia.org/wiki/Riemann–Stieltjes_integral here is a link if you wanna look in more detail

[vocal dome]

This makes so much sense

I’ve never seen that notation though

[woven copper]

Yes this is what are we learning

[vocal dome]

Epic

Well I suppose it’s not rly ftcp1

Cause it’s inside

I suppose the ftcp1 gets rid of the constant or whatever

If your evaluating an indefinite integral

But idk

[woven copper]

We will move on to area calculation soon said my teacher idk what that means but i know integral is about calculating an area of a graph

[vocal dome]

Yeah

That’s the basic definition

You might learn

,w disc method

[delicate cargo]

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Requested by axkyn

[vocal dome]

Man

Disc method is like pi times integral of (f(x))^2 dx

Good stuff

That’s for later though

[red jolt]

I thought D meant derivative

not d

[vocal dome]

It probably does mean deravative

[red jolt]

Like I’ve seen D(f(x)) before

[woven copper]

Well i hope i can enjoy it

[vocal dome]

You will

Ah so that’s why you don’t know much u sub

You’ll probably learn about left and right riemann sums

And trapezoid

[woven copper]

i should get some sleep i guess i have an exam on limits Derivative functions and integral like 7 hours later

[red jolt]

You basically just did that earlier

[woven copper]

Yeah I am just a starter

[vocal dome]

Mhm

Learn reverse power rule

And ibp

[woven copper]

i will check them

[red jolt]

You’re integrating between x = 1 and x = 2, meaning you’re finding the curve between the function and x-axis, between x = 1 and x = 2

So your answer, 45/8, just means the area enclosed between the curve and the x axis is 45/8 units squared

[vocal dome]

Reverse power rule is kinda fun im ngl: int of x^n dx where n does not equal zero, x^(n+1)/(n+1)

[final lodge]

d means infitesimally small change in

[vocal dome]

So it’s just like ftcp2

[red jolt]

I think it’s literally what that is

b
∫ f(x) = F(b) - F(a)
a
where F is the antiderivative of f

[vocal dome]

Yeah

[woven copper]

ohhh

i got it

[vocal dome]

There are these things called indefinite and definite integrals

Definite integrals you do ftcp2 and solve for area

[woven copper]

it was an question in yks 2024(university exam for turkey)

[vocal dome]

Indefinite you solve for int and do+C

[vocal dome]

[woven copper]

yeah i know about them i guess

i can calculate some definite integrals

[vocal dome]

That’s good

[woven copper]

this year i will enter university exam i am not so hopeful for maths but science section(physics chemistry and biology) may save me i hope

[vocal dome]

How old are you by the way

[woven copper]

17

[vocal dome]

[woven copper]

thanks y'all for helping

[vocal dome]

No prob, good luck on exams

[woven copper]

ty

[woven copper]

okay uh

i was not fucking able to do anything on my exam paper

just a few questions

i am on my teachers mercy rn

[vocal dome]

Any questions you need help understanding

[woven copper]

i couldn't translate it but i will trust to google for it wait a min

is that understandable?

chat gpt exists for a reason

[vocal dome]

So we need to know K(t)