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Linear by Quadratic...

Eh?

But, how exactly am I supposed to do this one?

If you put ax2 + bx + c = y then it helps or not??

uhh... what about the top - we just substitute using the quadratic formula in that case?

bring everything on the bottom to the top... then integration by parts?

uhh - I'm not sure that will work >.<

why not...

ohh

http://integral-table.com/downloads/single-page-integral-table.pdf
#16, btw

ahhh that got me thinkin... let me take another look

well log came from 1/x

Yes.

that looks like a big u sub

Uh, got any ideas where to start htough?

one sec

kay

just by the looks w/o really thinking about it, it looks like they let the bottom = u

then factor out a 2a

1/2a *

wait wtf

lol nvm i thought the second half was the next step

thats a tricky one i need a piece of paper for that one lol

okay lol. Thanks for helping :P

http://www.wolframalpha.com/input/?i=int+x%2F+%28ax2+%2B+bx+%2B+c%29

that way is crazzyyyy tho lol

its the same just written different

x = 1/2(2x + b/a) - 1/2 (b/a)
make two fractions ... and use the usual approach

^^^ thats what w.a did too

Okay. any way to reduce it to the form seen in the integral table?

probably not

one is going to be log
another ... complete squares (a+sqrt(b/4a))^2 - (b/4a-c)

this is in standard form ... you should be able to evaluate this.

Wait, I can do it by completing the square as well?

oh wow. this integral - sqrt(tan x) - is a freaking pain...

quite a bit ... assuming c/a > b/4a

thats when the mathematicians come in handy =P

yw inky.. you taking calc 2 over the summer??

I'm trying to finish calc 3 and linear algebra and diff equations over the summer >.<

crazyyy

that is a lot of material to learn!!

Yea, hopefully I can finish it.

I got faith!! where about are you in diffs?

Haven't even started LOL

haha I see I see

well, I skimmed the variables seperatble and the first order linear ODE I think

yea seps will seem very natural

linear first order with the integrating factor is tricky to understand at first... but easy to do

alright - I have to learn how to integrate these nasty partial fractions first though haha :P

haha just remember, If your integrating with respect to y , all the other variables are constant!

keep repeating that in your head as you run through your derivative..

pretend that all the other letters are just numbers and youll be golden!

didn't you see what i last posted earlier inky?

uhh what did you post?