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whatisthequestion

  • 2 years ago

Evaluate the integral. The integral will be entered below. The title of this section is Intergration of Rational Fractions by Partial Fractions

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  1. whatisthequestion
    • 2 years ago
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    \[\int\limits_{}^{}\frac{ x^2+2x-1 }{ x^3-x }dx\]

  2. whatisthequestion
    • 2 years ago
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    I can simplify it down to \[\int\limits_{}^{}\frac{ A }{ x }+\frac{ B }{ x-1 }+\frac{ C }{ x+1 }\] but get lost when solving for A, B and C

  3. whatisthequestion
    • 2 years ago
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    oops forgot a dx there

  4. Best_Mathematician
    • 2 years ago
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    do u want answer or explanation

  5. whatisthequestion
    • 2 years ago
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    explanation my math teacher was very confusing when going over this section (thick accent)

  6. whatisthequestion
    • 2 years ago
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    I probably screwed up because its three terms now instead of two

  7. whatisthequestion
    • 2 years ago
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    I had \[x^2+2x-1=Ax+B(x-1)+C(x+1)\] which is obviously wrong

  8. Best_Mathematician
    • 2 years ago
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    i m lost

  9. whatisthequestion
    • 2 years ago
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    yea this method is past l'Hopital's rule which I think you said you did not know earlier so it might be a little higher than your current level of math course

  10. Best_Mathematician
    • 2 years ago
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    first factor the function

  11. whatisthequestion
    • 2 years ago
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    which I did getting x(x-1)(x+1) on the bottom

  12. Best_Mathematician
    • 2 years ago
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    yes that is true

  13. zepdrix
    • 2 years ago
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    \[\large \frac{x^2+2x-1}{x(x-1)(x+1)} \qquad =\qquad \frac{A}{x}+\frac{B}{x-1}+\frac{C}{x+1}\]You should set it up like this. It looks like you're on the right track. You just didn't multiply through correctly.

  14. zepdrix
    • 2 years ago
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    Multiply both sides by the denominator on the left. :O

  15. whatisthequestion
    • 2 years ago
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    O GOD top ten list of signs I need to go to bed

  16. whatisthequestion
    • 2 years ago
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    so the correct answer is \[x^2+2x-1=A(x+1)(x-1)+Bx(x+1)+Cx(x-1)\]\[=(A+B+C)X^2+(B-C)X-A\]\[A=1, B=1, C=-1\]

  17. zepdrix
    • 2 years ago
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    Yah that looks right :)

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