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Math Challenge

Discussion in 'BBS Hangout' started by Tree-Mac, Mar 22, 2009.

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  1. Tree-Mac

    Tree-Mac Member

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    How the heck do you integrate this?

    x dx/ (x^3 - 1) ...... (x^3 means "x cubed")

    I spent like 3 hours trying to solve this problem but couldn't do it. Thanks in advance. :confused:
     
    #1 Tree-Mac, Mar 22, 2009
  2. Royals Ego

    Royals Ego Member

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    I don't know. But can I ask what you did in those 3 hours?
     
    #2 Royals Ego, Mar 22, 2009
  3. Stevierebel

    Stevierebel Member

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    Nevermind. I might work on it if someone else doesn't give you an answer..
     
    #3 Stevierebel, Mar 22, 2009
  4. D-Lite

    D-Lite Member

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    lol i dont think its that simple
     
    #4 D-Lite, Mar 22, 2009
  5. D-Lite

    D-Lite Member

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    EDIT..

    you did not see the x*dx DIVIDED BY (x^3-1)


    in any case.. i used an online integrator and that answer that popped up was too complicated.. im not gonna touch this one
     
    #5 D-Lite, Mar 22, 2009
  6. Tree-Mac

    Tree-Mac Member

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    From first look, I thought it was partial fractions, but it's not. And obviously substitution doesn't work either. I'm thinking maybe trigonometric substitution, but how do you make it into a^2 + x^2 form? I don't know.
     
    #6 Tree-Mac, Mar 22, 2009
  7. D-Lite

    D-Lite Member

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    alright nvm ill try, how about trig sub:


    x^2=sec(x)?

    then use the identity tan(x)^2=sec(x)^2-1

    dunno if that works
     
    #7 D-Lite, Mar 22, 2009
  8. D-Lite

    D-Lite Member

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    yea this should work, remember to find the new dx as well
     
    #8 D-Lite, Mar 22, 2009
  9. Tree-Mac

    Tree-Mac Member

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    Can you elaborate? This is what I got if I substitute like you said:

    Sqrt (sec x) dx/ ((Sqrt (sec x) * (tan^2(x) - 1)-1) ........

    This still doesn't work because how do you take care of the denominator? It's even messier than the original problem.
     
    #9 Tree-Mac, Mar 22, 2009
    Last edited: Mar 22, 2009
  10. D-Lite

    D-Lite Member

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    ahh my bad, its way too early in the morning.

    I messed up in the beginning. What i wrote does not work at all. Back to the drawing board because i have no clue what to do.
    :mad:
     
    #10 D-Lite, Mar 22, 2009
  11. Mr. Clutch

    Mr. Clutch Member

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    :confused:


    Does anyone know what these guys are talking about?
     
    #11 Mr. Clutch, Mar 22, 2009
  12. Andy3000

    Andy3000 Member

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    What the hell is "x"?
     
    #12 Andy3000, Mar 22, 2009
  13. D-Lite

    D-Lite Member

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    its been a while since ive done this stuff..

    im gonna let you try this one if you want, because i have to go

    x^3-1 factors into (x-1)*(X^2+x+1)

    there is a trick in integration where

    x/a= (x-1+1)/a

    so by applying that

    (x-1+1)/[(x-1)*(X^2+x+1)]

    split them up into two different fractions

    (x-1)/[(x-1)*(X^2+x+1)] + 1/[(x-1)*(X^2+x+1)]

    in the first term, the (x-1) cancel out

    you can try this

    peace.
     
    #13 D-Lite, Mar 22, 2009
  14. TheRealist137

    TheRealist137 Member

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    I thought you needed to use substitution.

    u = x^3 -1
    du = 3x^2 dx

    Take the 3 out

    so it becomes

    x^2 dx / (x^3 -1)

    or

    du/u

    which makes it

    3 ln (x^3-1) + C

    I think that's what the answer is, not entirely sure that it's right.
     
    #14 TheRealist137, Mar 22, 2009
  15. TheRealist137

    TheRealist137 Member

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    Actually, I don't think it's right, I had x^2 dx on the top while the question was only x dx.

    My bad.
     
    #15 TheRealist137, Mar 22, 2009
  16. Xcellerator

    Xcellerator Member

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    On my ti-89 I get:

    [ln( (x - 1)^2 / abs(x^2 + x + 1) ) / 6] + [ sqrt(3) * invtan(sqrt(3) *(2x + 1)) / 3]
     
    #16 Xcellerator, Mar 22, 2009
  17. Northside Storm

    Northside Storm Member

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    I would guess factoring the x^3-1 into an x^2 form, then using u substitution with the factor being 1/2.

    I'm too lazy to actually check if that works though...and it's probably a bit too simple considering the answers getting churned out lol.
     
    #17 Northside Storm, Mar 22, 2009
  18. Tree-Mac

    Tree-Mac Member

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    Thanks D-Lite! What is that x/a trick? Anyone else can do this problem?
     
    #18 Tree-Mac, Mar 24, 2009
  19. MadMax

    MadMax Member

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    I got her numbah.

    How ya like them apples???
     
    #19 MadMax, Mar 24, 2009
  20. JuanValdez

    JuanValdez Member

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    Bad thread title. This isn't a challenge so much as help doing your homework.
     
    #20 JuanValdez, Mar 24, 2009
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