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tux

  • 4 years ago

What I am doing wrong? integrate dx/(x^3-4x) Rewrite denominator as x*(x^2-4) and then use integration by partial fractions. (A/x) + (Bx+C)/(x^2-4) 1=A*(x^2-4)+(Bx+C)*x A=-1/4 B=1/4 C=0 After that I have to integrate -1/4*integral dx/x Result is -1/4ln(x) Second integral is (1/4*x)/(x^2-4) As result I get 1/8*ln(x^2-4) My final result is -1/4ln(x)+1/8*ln(x^2-4)+C Is my result correct?

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  1. slaaibak
    • 4 years ago
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    x^2 - 4 = (x - 2)(x + 2)

  2. slaaibak
    • 4 years ago
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    So it becomes A/x + B/(x+2) + C/(x-2)

  3. tux
    • 4 years ago
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    Can I use (Bx+C)/(x^2-4)?

  4. amistre64
    • 4 years ago
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    x(x-2)(x+2)

  5. tux
    • 4 years ago
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    When I take x(x-2)(x+2) then A=-1/4 B=1/8 C=1/8 and result is \[-1/4*\ln(x)+1/8\ln(x-2)+1/8\ln(x+2)\]

  6. slaaibak
    • 4 years ago
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    correct

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