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inkyvoyd
 3 years ago
Integrate
\(\Huge \frac{x}{ax^2+bx+c}\)
inkyvoyd
 3 years ago
Integrate \(\Huge \frac{x}{ax^2+bx+c}\)

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waterineyes
 3 years ago
Best ResponseYou've already chosen the best response.0Linear by Quadratic...

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0But, how exactly am I supposed to do this one?

waterineyes
 3 years ago
Best ResponseYou've already chosen the best response.0If you put ax2 + bx + c = y then it helps or not??

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0uhh... what about the top  we just substitute using the quadratic formula in that case?

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry guys, I'm not even sure where to start with this integral. I can't find it in my book either >.<

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1bring everything on the bottom to the top... then integration by parts?

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0uhh  I'm not sure that will work >.<

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0All the related integrals had something to do with trig sub and inverse trig functions, but i can't find this case.

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0I know what the answer is (from an integral table), and it's logarithmic+trigonometric. I have no idea where to start though

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0http://integraltable.com/downloads/singlepageintegraltable.pdf #16, btw

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1ahhh that got me thinkin... let me take another look

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1well log came from 1/x

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1that looks like a big u sub

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Uh, got any ideas where to start htough?

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1just by the looks w/o really thinking about it, it looks like they let the bottom = u

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1lol nvm i thought the second half was the next step

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1thats a tricky one i need a piece of paper for that one lol

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0okay lol. Thanks for helping :P

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=int+x%2F+%28ax2+%2B+bx+%2B+c%29

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1that way is crazzyyyy tho lol

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0lol  but the answer is different from the integral table :S the result is too complicated lol. I'm using some constants for the integral that will make it even more nasty x.x

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1its the same just written different

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3x = 1/2(2x + b/a)  1/2 (b/a) make two fractions ... and use the usual approach

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1^^^ thats what w.a did too

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Okay. any way to reduce it to the form seen in the integral table?

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0once i substitute my values in, it is still an intermediate result  I still have to do two more substitutions, and I'm not sure I can do the algebra without going insane.

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3one is going to be log another ... complete squares (a+sqrt(b/4a))^2  (b/4ac)

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3this is in standard form ... you should be able to evaluate this.

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, I can do it by completing the square as well?

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3\[ \frac1{2a}\frac{x + b/a}{x + b/a x+c/a}  \frac1{2a}\frac{ b/a}{(x + \sqrt{b/4a})^2  (b/4ac/a)}\]

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0oh wow. this integral  sqrt(tan x)  is a freaking pain...

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3quite a bit ... assuming c/a > b/4a

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1yea just about all realistic functions are either extremely tedious or impossible to solve by hand. When it comes to practical application, we usually just have computers solve or approximate the solution.

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Ugh, I give up. I'm tired of this integral lol. I'll look into it more tomorrow. Thanks though, @experimentX and @eyust707

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1thats when the mathematicians come in handy =P

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1yw inky.. you taking calc 2 over the summer??

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0I'm trying to finish calc 3 and linear algebra and diff equations over the summer >.<

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1that is a lot of material to learn!!

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Yea, hopefully I can finish it.

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1I got faith!! where about are you in diffs?

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0Haven't even started LOL

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0well, I skimmed the variables seperatble and the first order linear ODE I think

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.3It's just a substitution ... reduces to the form \[ \int \frac1 {x^2 + a^2}dx\] or, \[ \int \frac 1{x^2  a^2}dx\] assuming first, wolf calculates 2/a arctan(x/a)

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1yea seps will seem very natural

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1linear first order with the integrating factor is tricky to understand at first... but easy to do

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1youll prob see frustrating word problems but dont let them scare you.. they always work out to be quite simple

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0alright  I have to learn how to integrate these nasty partial fractions first though haha :P

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1haha just remember, If your integrating with respect to y , all the other variables are constant!

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1keep repeating that in your head as you run through your derivative..

eyust707
 3 years ago
Best ResponseYou've already chosen the best response.1pretend that all the other letters are just numbers and youll be golden!

dpaInc
 3 years ago
Best ResponseYou've already chosen the best response.0didn't you see what i last posted earlier inky?

inkyvoyd
 3 years ago
Best ResponseYou've already chosen the best response.0uhh what did you post?
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