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Thread: integration (x^2-x+6)/(x^3+3x) dx by parts

  1. #1

    integration (x^2-x+6)/(x^3+3x) dx by parts

    integrate (x^2-x+6)/(x^3+3x) dx

    I get stuck when im trying to find what a b and c should be.

  2. #2
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    I don't know what a, b or c are and it looks like you've tried to include an image; could you edit the post please so that I can help?

  3. #3
    Elite Member stapel's Avatar
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    Re: integration (x^2-x+6)/(x^3+3x) dx by parts

    Quote Originally Posted by summergrl
    integrate (x^2-x+6)/(x^3+3x) dx

    I get stuck when im trying to find what a b and c should be.
    What "a", "b", and "c"? There is only "x" in your integrand.

    Please reply with clarification, including a clear listing of all of your work and reasoning so far.

    Thank you.

    Eliz.

  4. #4
    sorry...the image was there by mistake.
    I am pretty sure I need to use integration by parts and we use A, B, and C.
    So so far i seperated it into
    A/X + (Bx+C)/(x^2+3)

  5. #5
    Senior Member skeeter's Avatar
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    I think you mean partial fractions, not integration by parts.

    [tex]\L \frac{x^2 - x + 6}{x(x^2 + 3)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 3}[/tex]

    [tex]\L \frac{x^2 - x + 6}{x(x^2 + 3)} = \frac{A(x^2+3)}{x(x^2+3)} + \frac{x(Bx + C)}{x(x^2 + 3)}[/tex]

    [tex]\L x^2 - x + 6 = A(x^2 + 3) + x(Bx + C)[/tex]

    [tex]\L x^2 - x + 6 = (A + B)x^2 + Cx + 3A[/tex]

    equate coefficients ...

    [tex]\L A + B = 1[/tex]
    [tex]\L C = -1[/tex]
    [tex]\L 3A = 6[/tex]

    can you finish?

  6. #6
    oops! i keep on mixing those two names up.
    how do you know A+b=1?

  7. #7
    Senior Member skeeter's Avatar
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    [tex]\L x^2 - x + 6 = (A+B)x^2 + Cx + 3A[/tex]

    look at the left side of the equation ... what is the coefficient of x<sup>2</sup>?

    look at the right side of the equation ... what is the coefficient of x<sup>2</sup>?

    now set the coeffcients equal.

  8. #8
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    If you know about complex numbers you can do it much faster...

  9. #9
    Senior Member skeeter's Avatar
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    Quote Originally Posted by Count Iblis
    If you know about complex numbers you can do it much faster...
    ... and if only pigs could fly.

  10. #10
    okay thanks! i understand that part now...so I got B=-1, C=-1, and A =2.
    then i get the integration of
    (2/x) - (x/x^2+3) - (1/x^2+3)
    and i get 2lnx - 1/2ln(x^2+3) but then i don't know how to do the third part. Does it have anything to do with arctan?

    p.s. whats this talk about pigs?? hehe

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