/sci/ - Science & Math

>>12456367
You can't do it either and are trying to bait /sci/ into answering.

Get filtered brianlet.

>>12456377
i did it though :)

>>12456367
This is simple trigonometry.

>>12456411
i know and it's baffling how my classmates can't do it
they even look down on me for knowing calculus

>>12456367
I have not done manual integrals in 10 years but sure some kind of trig substitution. Can i check trig tables or is that cheating? Is Mathematica cheating? If i have to think too much and the answer doesnt come right away is that cheating too?

>>12456367
Simpson's rule.

There, solved it - and exactly, too.

log(3/2)/2 the schizo shit cancels out

>>12456446
based but i left it at 1/2(log3-log2) because our teacher doesn't allow us to transform substitution into division for the logs

>>12456444
i haven't studied that yet


>>12456442
yes to all of them

>doing integrals by hand

https://www.wolframalpha.com/input/?i=integral+from+2+to+3+of+y%3D1%2F%28x%5E2-1%29

>>12456448
>doesn't allow us to transform
lol i like to try to reduce everything into the least number of symbols, like code golf

>>12456452
lmfao filtered by syntax

>studied calculus for two years
>doesn't know what a partial fraction expansion is
And you think you're superior to anyone?

Is there an easiest way than partial fraction decomposition?

>>12456462
memorization

>>12456367
Holy fuck i always forget theoretical justification for partial fractions.

>>12456367
isn't that integration by substitution? that shit i still know...

>>12456367
Where do you study, anon?

>>12456596
Highschool

>>12456367
I've been studying calculus for no time at all and I don't understand it.
Mathematically speaking, who was in the wrong here?

>>12456581
it is

>>12456596
high school in romania
this guy isn't me >>12456606


>>12456614
everyone

>>12456462
this >>12456570
i know all of the common integrals by heart at this point

I'm OP

>>12456614
its easy just take u = x^2 - 1. take derivative du/dx=2x substitute dx = du/2x integrate (you get ln 2x or something) then sub back in. ends up ln (2x^2 -2) or something

>>12456630
you don't need to do that, the integral is just a common formula :

[math] int(1/(x^2-a))= 1/(2*a) * ln(abs((x-a)/(x+a)))+c [/math]

sorry idrk latex :P

>>12456636
that looks wrong tho

>>12456647
that's the formula i know
this is what i wanted to write

>>12456630
nevermind i fucked up somewhere

>>12456636
looks like you need a trig substitution like someone already said

>>12456630
Last time I saw mental gymnastics of this level was on CNN

>>12456671
ya ya ya fuck off. i already admitted i was wrong

>>12456662
i don't think it's necessary doe
like you just take a=1 and then you write the formula

>>12456688
you should know how to integrate that without a formula to pass 1st year calculus

>>12456630
What is dx and du to you? A number?

>>12456733
Two numbers?

>>12456367
What is the step by step for this?

Highschool dropout reporting in

>>12456774
[math] \frac{1}{x2-1} = \frac{1}{2}.\frac{1}{x-1} - \frac{1}{2}.\frac{1}{x+1} [/math] then use integer of [math] \frac{u'}{u} [/math]

>>12456870
my mistake it's [math] \frac{1}{x^{2}-1} = \frac{1}{2}.\frac{1}{x-1} - \frac{1}{2}.\frac{1}{x+1} [/math]

>>12456367
https://youtu.be/yOfgZ_rJOos

It's not really math. It's more like memorizing tricks.

>>12456367
Imagine ever doing an integral by hand post-high school.

>>12456630
Substituting dx=du/2x leaves you with an x in the integrand.

>>12456367
I have a BS in math and I sometimes forget how to do that shit. Just plug it into wolfram alpha, memorizing a bunch of integration tricks doesn't make you smart or even good at math. It just means you're autistic

>>12456367
So you are bragging that you are better than your classmates on an anonymous anime board.

are you an IB fag?? if u are fuck you

>>12456875
Why is your name heliogabelus?
He was a tranny who sacrificed children daily
He even kidnapped kids from the wealthiest and most educated families to cause the most suffering

>>12456367
>>12456446
>>12456448
I don't understand, you guys must be either under age or retarded to not know this. Pic related is the simple answer btw.

>>12458235
I forgot to mention you can simplify to give ln 6^0.5/2 if you wanted

>>12456367
There is absolutely no use in memorizing the table of integrals for retarded functions that don't even exist. You can look it up any time. If world goes to shit that integral will be least of your problems.

What's the trig approach for that?

>>12458320
In the region (-1,1) the integral is -arctanh(x) so you can figure it out if you torture yourself for awhile for no reason. jk it seems fun might try it if I feel cute

>>12456367
>for 2 years
jesus how long does it fucking take to figure out how to do fucking algebra you fucking retards.
what retarded backwards cunt are you from?
I learned all of calculus in under a year, why? because it's for fucking babies.

wow...

I haven't done calc in years.
Am I a dweeb that I did this by partial fractions?

I was electric at calculus in High School

>>12458304
Why would you need to memorize anything? This is basic ass integration by substitution. OP's classmates are retarded, but OP is a faggot for bragging about being able to do simple calculus.

>>12457012
Wrong. It builds up mathematical skill. Part of math is pattern recognition and symbolic manipulation which doing integrals by hand is an excellent exercise. Also improves memory.

>>12458538
>which doing integrals by hand is an excellent exercise.
no its not you fucking retard
all practicing integrals does is makes you better at integrals
it doesnt make you better at pattern recognition you mong

>>12458340
>arctanh(x)
Please use the proper term artanh. It represents the area of an ellipse or hyperbola, not the arc of a circle.

>>12458235
that's what i got doe

>>12458304
i'm in HS so it's mandatory to learn tables by heart
>>12458357
romania

>>12456367
imagine being filtered by partial fractions

Three years ago, I knew how to perform trigonometric/hyperbolic substitutions for integrals. I knew the traps involved in the inverse trig functions. I pretty much got perfect grades in Calc II. Now I've forgotten it all, with only the conceptual understanding of integrals retained. I guess in a certain sense the understanding is permanent: I could skim through Calc II material as a refresher and master it in a tenth of the time it took originally. Still, feels bad, man.

>>12459451
>romania
at least the women are hot.

>>12459467
yeah yeah i'm retarded i know shut up

>>12459511
but they're idiots

>>12458249
no, that's not the same and stop using ln for log

>>12456367
>second year math student
>completely forgot how to do partial fractions and was genuinely stumped on this question for like 10 minutes
for fucks sake, bros...

tried doing it by turning this function into polynomial but I got 1/2 ( (ln x -1) - (ln x +1) )
wolfram for some reason gives me 1 - x in first ln, why?
https://www.wolframalpha.com/input/?i=integral+1%2F%28x%5E2+-+1%29

>>12460588
what you got is right, wolfram's answer is wrong
idk why, symbolab also gave me a wrong answer

>>12456367
My Calc II prof said that partial fractions is one of the key reasons the course even exists.

>>12460659
Wolfram isn't wrong you fucking disphit.
>>12460588
This is just artanh. The integral in OP is well known as the artanh integral.
>>12460659
faggot

>>12456367

Just draw a bunch of skinny rectangles under the curve and estimate the area.

It's not hard.

Not like most functions have nice antiderivatives anyway. Integral calculus is a waste of time.

hmmm,you can't divide by zero

>>12456652
[eqn] \int \dfrac{1}{x^2-a^2} \; dx = \dfrac{1}{2a} \; \ln\left|\dfrac{x-a}{x+a}\right| + C [/eqn]

right click, show math as Tex, \; is for spacing

>>12461679
lol cope and seethe wolframoid

>>12461697
>Integral calculus is a waste of time.
big truth

>>12462743
thanks i need to brush up on my latex :/

>>12456367
Simple trig identity. Evaluate the antiderivative you get from the identity at the integration limits.

>>12463077
what trig identity?

>>12463076
there's nothing to cope about, wolfram was correct and if you can't see why you're a total retard

>>12456367
integrals are just [math]\frac{d^{-1}}{dx^{-1}}[/math]

>>12463357
think he means these hypertrig identities
https://en.wikipedia.org/wiki/Hyperbolic_functions#Derivatives

I was gonna berate you op for making this shit thread but after reading

>>12456442
>>12456444
>>12456452
>>12456570
>>12456577
>>12456581
>>12456614
>>12456630
>>12456636
>>12456662
>>12456671
>>12456933
>>12457012
>>12458304
>>12458320
>>12458357
>>12459451
>>12460065
>>12463076
>>12463077
>>12463862

I am actually quite astonished

>inb4 hurr durr i was only pretending

>>12456367
>le multiply two polynomials trick
>master at calculus

>>12465145
Didn't study calc because it was boring, cope

>>12456462
tanh

>>12456367
It's just fraction decomposition and the bottom polynomial is as simple as they come. If you can't do this in your head without knowing a specific formula in advance you are probably fucking retarded

>>12456367
It's ok OP someday when you've forgoten all this shit some HS kid will clown you for it and the cycle will be complete

>>12461697
>differential equations is a waste of time
what did he mean by this

>>12461697
fuck /sci/

>>12466113

Numerical methods with existence/convergence proofs are the only good math.

>>12456367
there's nothing to 'do' here. this is just a result you can quote

>>12456367
What function has as its derivative
[math]
/frac{1}{x^2 -1}[/math]?
[math]
f(x) = /frac{1}{2}/log/left( /frac{x-1}{x+1}/right)
[/math]
Of course