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inkyvoyd

Integrate \(\Huge \frac{x}{ax^2+bx+c}\)

  • one year ago
  • one year ago

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  1. waterineyes
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    Linear by Quadratic...

    • one year ago
  2. inkyvoyd
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    Eh?

    • one year ago
  3. inkyvoyd
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    But, how exactly am I supposed to do this one?

    • one year ago
  4. waterineyes
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    If you put ax2 + bx + c = y then it helps or not??

    • one year ago
  5. inkyvoyd
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    uhh... what about the top - we just substitute using the quadratic formula in that case?

    • one year ago
  6. inkyvoyd
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    Sorry guys, I'm not even sure where to start with this integral. I can't find it in my book either >.<

    • one year ago
  7. eyust707
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    bring everything on the bottom to the top... then integration by parts?

    • one year ago
  8. inkyvoyd
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    uhh - I'm not sure that will work >.<

    • one year ago
  9. eyust707
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    why not...

    • one year ago
  10. inkyvoyd
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    All the related integrals had something to do with trig sub and inverse trig functions, but i can't find this case.

    • one year ago
  11. eyust707
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    ohh

    • one year ago
  12. inkyvoyd
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    I know what the answer is (from an integral table), and it's logarithmic+trigonometric. I have no idea where to start though

    • one year ago
  13. inkyvoyd
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    http://integral-table.com/downloads/single-page-integral-table.pdf #16, btw

    • one year ago
  14. eyust707
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    ahhh that got me thinkin... let me take another look

    • one year ago
  15. eyust707
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    well log came from 1/x

    • one year ago
  16. inkyvoyd
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    Yes.

    • one year ago
  17. eyust707
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    that looks like a big u sub

    • one year ago
  18. inkyvoyd
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    Uh, got any ideas where to start htough?

    • one year ago
  19. eyust707
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    one sec

    • one year ago
  20. inkyvoyd
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    kay

    • one year ago
  21. eyust707
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    just by the looks w/o really thinking about it, it looks like they let the bottom = u

    • one year ago
  22. eyust707
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    then factor out a 2a

    • one year ago
  23. eyust707
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    1/2a *

    • one year ago
  24. eyust707
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    wait wtf

    • one year ago
  25. eyust707
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    lol nvm i thought the second half was the next step

    • one year ago
  26. eyust707
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    thats a tricky one i need a piece of paper for that one lol

    • one year ago
  27. inkyvoyd
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    okay lol. Thanks for helping :P

    • one year ago
  28. eyust707
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    http://www.wolframalpha.com/input/?i=int+x%2F+%28ax2+%2B+bx+%2B+c%29

    • one year ago
  29. eyust707
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    that way is crazzyyyy tho lol

    • one year ago
  30. inkyvoyd
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    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

    • one year ago
  31. eyust707
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    its the same just written different

    • one year ago
  32. experimentX
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    x = 1/2(2x + b/a) - 1/2 (b/a) make two fractions ... and use the usual approach

    • one year ago
  33. eyust707
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    ^^^ thats what w.a did too

    • one year ago
  34. inkyvoyd
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    Okay. any way to reduce it to the form seen in the integral table?

    • one year ago
  35. eyust707
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    probably not

    • one year ago
  36. inkyvoyd
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    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.

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

    • one year ago
  38. experimentX
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    this is in standard form ... you should be able to evaluate this.

    • one year ago
  39. inkyvoyd
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    Wait, I can do it by completing the square as well?

    • one year ago
  40. experimentX
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    \[ \frac1{2a}\frac{x + b/a}{x + b/a x+c/a} - \frac1{2a}\frac{ b/a}{(x + \sqrt{b/4a})^2 - (b/4a-c/a)}\]

    • one year ago
  41. inkyvoyd
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    oh wow. this integral - sqrt(tan x) - is a freaking pain...

    • one year ago
  42. experimentX
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    quite a bit ... assuming c/a > b/4a

    • one year ago
  43. eyust707
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    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.

    • one year ago
  44. inkyvoyd
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    Ugh, I give up. I'm tired of this integral lol. I'll look into it more tomorrow. Thanks though, @experimentX and @eyust707

    • one year ago
  45. eyust707
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    thats when the mathematicians come in handy =P

    • one year ago
  46. eyust707
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    yw inky.. you taking calc 2 over the summer??

    • one year ago
  47. inkyvoyd
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    I'm trying to finish calc 3 and linear algebra and diff equations over the summer >.<

    • one year ago
  48. eyust707
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    crazyyy

    • one year ago
  49. eyust707
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    that is a lot of material to learn!!

    • one year ago
  50. inkyvoyd
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    Yea, hopefully I can finish it.

    • one year ago
  51. eyust707
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    I got faith!! where about are you in diffs?

    • one year ago
  52. inkyvoyd
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    Haven't even started LOL

    • one year ago
  53. eyust707
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    haha I see I see

    • one year ago
  54. inkyvoyd
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    well, I skimmed the variables seperatble and the first order linear ODE I think

    • one year ago
  55. experimentX
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    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)

    • one year ago
  56. eyust707
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    yea seps will seem very natural

    • one year ago
  57. eyust707
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    linear first order with the integrating factor is tricky to understand at first... but easy to do

    • one year ago
  58. eyust707
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    youll prob see frustrating word problems but dont let them scare you.. they always work out to be quite simple

    • one year ago
  59. inkyvoyd
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    alright - I have to learn how to integrate these nasty partial fractions first though haha :P

    • one year ago
  60. eyust707
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    haha just remember, If your integrating with respect to y , all the other variables are constant!

    • one year ago
  61. eyust707
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    keep repeating that in your head as you run through your derivative..

    • one year ago
  62. eyust707
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    pretend that all the other letters are just numbers and youll be golden!

    • one year ago
  63. dpaInc
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    didn't you see what i last posted earlier inky?

    • one year ago
  64. inkyvoyd
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    uhh what did you post?

    • one year ago
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