inkyvoyd
  • inkyvoyd
Integrate \(\Huge \frac{x}{ax^2+bx+c}\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Linear by Quadratic...
inkyvoyd
  • inkyvoyd
Eh?
inkyvoyd
  • inkyvoyd
But, how exactly am I supposed to do this one?

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More answers

anonymous
  • anonymous
If you put ax2 + bx + c = y then it helps or not??
inkyvoyd
  • inkyvoyd
uhh... what about the top - we just substitute using the quadratic formula in that case?
inkyvoyd
  • inkyvoyd
Sorry guys, I'm not even sure where to start with this integral. I can't find it in my book either >.<
eyust707
  • eyust707
bring everything on the bottom to the top... then integration by parts?
inkyvoyd
  • inkyvoyd
uhh - I'm not sure that will work >.<
eyust707
  • eyust707
why not...
inkyvoyd
  • inkyvoyd
All the related integrals had something to do with trig sub and inverse trig functions, but i can't find this case.
eyust707
  • eyust707
ohh
inkyvoyd
  • inkyvoyd
I know what the answer is (from an integral table), and it's logarithmic+trigonometric. I have no idea where to start though
inkyvoyd
  • inkyvoyd
http://integral-table.com/downloads/single-page-integral-table.pdf #16, btw
eyust707
  • eyust707
ahhh that got me thinkin... let me take another look
eyust707
  • eyust707
well log came from 1/x
inkyvoyd
  • inkyvoyd
Yes.
eyust707
  • eyust707
that looks like a big u sub
inkyvoyd
  • inkyvoyd
Uh, got any ideas where to start htough?
eyust707
  • eyust707
one sec
inkyvoyd
  • inkyvoyd
kay
eyust707
  • eyust707
just by the looks w/o really thinking about it, it looks like they let the bottom = u
eyust707
  • eyust707
then factor out a 2a
eyust707
  • eyust707
1/2a *
eyust707
  • eyust707
wait wtf
eyust707
  • eyust707
lol nvm i thought the second half was the next step
eyust707
  • eyust707
thats a tricky one i need a piece of paper for that one lol
inkyvoyd
  • inkyvoyd
okay lol. Thanks for helping :P
eyust707
  • eyust707
http://www.wolframalpha.com/input/?i=int+x%2F+%28ax2+%2B+bx+%2B+c%29
eyust707
  • eyust707
that way is crazzyyyy tho lol
inkyvoyd
  • inkyvoyd
lol - 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
  • eyust707
its the same just written different
experimentX
  • experimentX
x = 1/2(2x + b/a) - 1/2 (b/a) make two fractions ... and use the usual approach
eyust707
  • eyust707
^^^ thats what w.a did too
inkyvoyd
  • inkyvoyd
Okay. any way to reduce it to the form seen in the integral table?
eyust707
  • eyust707
probably not
inkyvoyd
  • inkyvoyd
once 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
  • experimentX
one is going to be log another ... complete squares (a+sqrt(b/4a))^2 - (b/4a-c)
experimentX
  • experimentX
this is in standard form ... you should be able to evaluate this.
inkyvoyd
  • inkyvoyd
Wait, I can do it by completing the square as well?
experimentX
  • experimentX
\[ \frac1{2a}\frac{x + b/a}{x + b/a x+c/a} - \frac1{2a}\frac{ b/a}{(x + \sqrt{b/4a})^2 - (b/4a-c/a)}\]
inkyvoyd
  • inkyvoyd
oh wow. this integral - sqrt(tan x) - is a freaking pain...
experimentX
  • experimentX
quite a bit ... assuming c/a > b/4a
eyust707
  • eyust707
yea 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
  • inkyvoyd
Ugh, I give up. I'm tired of this integral lol. I'll look into it more tomorrow. Thanks though, @experimentX and @eyust707
eyust707
  • eyust707
thats when the mathematicians come in handy =P
eyust707
  • eyust707
yw inky.. you taking calc 2 over the summer??
inkyvoyd
  • inkyvoyd
I'm trying to finish calc 3 and linear algebra and diff equations over the summer >.<
eyust707
  • eyust707
crazyyy
eyust707
  • eyust707
that is a lot of material to learn!!
inkyvoyd
  • inkyvoyd
Yea, hopefully I can finish it.
eyust707
  • eyust707
I got faith!! where about are you in diffs?
inkyvoyd
  • inkyvoyd
Haven't even started LOL
eyust707
  • eyust707
haha I see I see
inkyvoyd
  • inkyvoyd
well, I skimmed the variables seperatble and the first order linear ODE I think
experimentX
  • experimentX
It'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
  • eyust707
yea seps will seem very natural
eyust707
  • eyust707
linear first order with the integrating factor is tricky to understand at first... but easy to do
eyust707
  • eyust707
youll prob see frustrating word problems but dont let them scare you.. they always work out to be quite simple
inkyvoyd
  • inkyvoyd
alright - I have to learn how to integrate these nasty partial fractions first though haha :P
eyust707
  • eyust707
haha just remember, If your integrating with respect to y , all the other variables are constant!
eyust707
  • eyust707
keep repeating that in your head as you run through your derivative..
eyust707
  • eyust707
pretend that all the other letters are just numbers and youll be golden!
anonymous
  • anonymous
didn't you see what i last posted earlier inky?
inkyvoyd
  • inkyvoyd
uhh what did you post?

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