/sci/ - Science & Math

YouTube, that's what my sisters boyfriend did the other day anyhow and it worked for him.

it's all just memorization, and you likely won't use that shit after you're done with calc 2.

just memorize all the tests.

I wish you luck. Study, than you should be fine.

>>4510232
Unfortunately most people do just this.

>>4510232

Taylor series and sequences was my fav part of Calc 2.

Everyone else hated it and said they couldn't understand it, but i found it a lot more fun than anything else in calc 2

>>4510232
>cramming
>2012

http://patrickjmt.com/#calculus

Near the bottom of the second column.

>>4510221
>reading book
>come across problem
>Evaluate the indefinite integral as a power series
>Integral (atan(x^2)) dx

>>4510314
That's actually pretty simple.

You just start with a geometric series (1/1-r) and it's equivalent series representation sum n=0 to infinity r^n.

You can then manipulate it to look like the derivative of arctan, then you just integrate twice.

>>4510317
So... basically... I take the derivative of atan(x^2) => 2x/(1+x^4)

then i put that in a Geometric series form

then tack on two integral signs to the left of it?

>>4510326
It's better to work your way up from a geometric series.

Whenever you sub something into r on the left, sub it into r on the right

So first you would sub in (-x^4), and then multiply by x^2. Then integrate both sides twice.

>>4510326

yes, exactly. Good job man you're ready for the test.

>>4510329
Err, multiply by 2x

>>4510329
So, let me just get this straight:


integral( integral( 2x*Sum( 1/(1-(-x^4)) ) ) )

or is it

integral( integral( 2x*Sum( (-x^4)^n ) ) )

my mind is full of fuck

>>4510336

u r genuos

>>4510347
>>4510332
I'm on to you

>>4510336
First you have 1/1-r = Sum r^n
then 1/1+x^4 = sum (-1)^n(x^4n)
then 2x/1+x^4 = 2sum (-1)^n(x^(4n+1))
then you integrate
arctan(x^2)=2sum (-1)^n (x^(4n+2))/(4n+2)
then integreate again
and you get int arctan(x^2)dx =2sum(-1)^n (x^(4n+3))/(4n+3)(4n+2)

>>4510363
aww.. okay, now ic what you meant by both sides.

Thank you good sir