Halfway through Calc 3

Will you talk to me through an ear piece when I take my tests? There can be money in it for you.

There's a thing that's called something like " the conservation of difficulty", which means that most times, taking an alternative path makes things equally difficult. If you'll subtitute the whole thing with u, you'll have to sub it back right after in order to find out its integral. So just practice more i guess

just watch khan academy you stupid nigger

Americucks take more than 1 class of calculus? I only took calc in my first semester, followed up by linear algebra in my second.

there is calc 1, calc 2, calc 3 then differential equations which is kind of an extension of calculus in our curriculum

It's because we have calculus before uni. And it also depends on how many credits the course give. For instance the uni I'm changing to has 2x5 ECTS calculus courses.

all non retards have taken calculus 1 and 2 before college

In most American public schools they don't even offer calc 2 before college.

Who talked about schools? All non retards have taken calculus 1 and 2 before college, regardless of their schools offering them or not. Don't you know you can actually learn on your own?

You're confusing autists with non-retards, there is middle area, you are the former.

t. brainlet

honestly please die of cancer

t. jealous brainlet

Thats why america produces mathamaticians and engineers and europe produces jihadists.

Calc 3 is ODEs. Calc 4 is Multivariable, and then there are PDEs and Stochastic Calc.

It's just designed to simplify things for you.

>derive

ROOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

NEVER POST AGAIN FAGGOT

this is university specific, calc 2 was multivar at my uni and PDEs and stoch where a separate class that wasn't even called calculus.

Here are some notes lad
(1/3)

I just realized my resolution is super high so this is actually 2/2

Also, sorry if they look all over the place, but the examples may help.

...

they aren't called calculus here either, but are an extension of calculus by definition

OP here, just got back from classes, asked my professor at end of class to help explain it differently to me and he first asked how I got this far without knowing how to do basic integration techniques as a joke but then helped me, I think I have a basis of understanding now. I never understood how du could have a value, I never really understood what dx meant other than a symbol signifying the end of an integral, gonna get to work studying. By the way you write like a girl or a trap.

t. autist

You write like you're disabled, which if it's taken you this long to understand the basics you likely are.

>getting angered, defensive and delusional because of a comment on your handwriting

W-what happened user?

>assuming those emotions of me
>assuming im who you were responding to

Sad!

Sloppy seconds rule

t. dirty brainlet

OP here is the technique.

i'll use the example:

S(2x/(1+x^2))dx (S for integra symbol)

now this is a hard integral to do, but you can use U substitution to make it a lot easier.

let U be 1+x^2

now you have S(2x/(U))dx

this doesnt really help because the integral is still wrt x, not U. so lets find a du

U=1+x^2
du/dx = 2x
du=2xdx

our integral has a 2xdx on top! so lets put du instead

S(1/U)du

this is a lot easier, obviously this =ln(U)

now we just sub back in x^2+1

=ln(x^2 + 1)

see how nicely that worked out? the 2xdx became a du nice and clean. we cant evaluate the integral if we have any x's left over, after u sub you should be left with a function of u only.

like other anons said, the trick is to practice a lot. Just like trig identities, you will quickly gain an intuition of how to set up your sub so that it all works out.

Does that help?

What the fuck OP? The handwriting is fine and by no means "girly".

Yeah, that's nice.
But I don't understand any of it whatsoever. :(

Do you know the chain rule?

U-sub is just assuming that the integrand is a chain-rule derivative, and you have to reverse the process by finding the g(x) (which is the 'u' component.

If f(g(x)) differentiates to f'(g(x))g'(x), and u = g(x), then your integrand becomes f(u)(u').

You have to choose what u will be, then differentiate to get u'. u' should already be part of the integrand.

>why can't I just replace the entire integral with u and say I'm done?

you technically could do that, but there isn't only a u under the intregral. Every integral ends in a dx (or dt or du or whatever variable you are integrating under). If you let f(x)=u, then you must also have that f'(x)=du/dx which implies du=f'(x)dx.

Since we are taking the integral of u with respect to x, this doesn't make much sense, so we change it to respect with u by letting dx=du/f'(x). Therefore, if I do a u-sub, I must also divide the inside by the derivative of f(x). Since f'(x) may not always appear inside the integral or may not be a constant, u-sub typically relies on recognizing that a derivative of some term is present inside the integral.

Iktf, I'm a physics major and I'm taking Statistical Thermodynamics, Math Physics II and Emag II

It's not even a question of "just study more" it's a question of... "J-Jesus fucking Christ am I even smart enough for this?"