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Dido525

Evaluate the Intergal

  • one year ago
  • one year ago

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  1. Dido525
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    \[\int\limits_{}^{}\frac{ 2x^4-4x^3+13x^2-6x+10 }{ (x-2)(x^2-2x+5)^2 }dx\]

    • one year ago
  2. Dido525
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    I solved it using a beastly amount of partial fractions after solving a system of 5 equations. Please tell me there is another easier way.

    • one year ago
  3. DHASHNI
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    jus divide the numerator by x-2

    • one year ago
  4. Dido525
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    Why though? I have no reason to do long division.

    • one year ago
  5. DHASHNI
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    it is jus to simplify the question

    • one year ago
  6. Dido525
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    Hmm Okay... Let me see...

    • one year ago
  7. calmat01
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    Yep. it simplifies, reducing your amount of work.

    • one year ago
  8. calmat01
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    ok, maybe not. I really need a break. Making too many mistakes today. See you all later.

    • one year ago
  9. Dido525
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    Erm... THat doesent help O_o . I get: \[2x^3+13x+20 +\frac{ 50 }{ 2x^3+13x+20 }\]

    • one year ago
  10. satellite73
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    no it doesn't simplify but it has been cooked so that the partial fractions are nice integers

    • one year ago
  11. DHASHNI
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    yeah ^ he's right

    • one year ago
  12. Dido525
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    Ohh they are nice and all but even evaluating the damn partial fractions takes forever.

    • one year ago
  13. satellite73
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    there are some snap methods for getting some of them i think eliasaab who i have not seen here for a while had a snappy way of doing it

    • one year ago
  14. Dido525
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    So after the decomposition I get: \[\int\limits_{}^{}\frac{ 2 }{ x-2 }+\frac{ 4 }{ x^2-2x+5 }+\frac{ x }{ (x^2-2x+5)^2 }dx\]

    • one year ago
  15. Dido525
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    The first term is fine. It's the other two that take forever to integrate.

    • one year ago
  16. satellite73
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    all integration is a useless pain in the butt that is why they invented computers it is not math, it is wasted doodling

    • one year ago
  17. Dido525
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    Wolfram made I think... 9 substitutions. I refuse to do that.

    • one year ago
  18. TuringTest
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    @satellite73 D: blasphemy, integration is an art form!

    • one year ago
  19. satellite73
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    art who?

    • one year ago
  20. satellite73
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    waste a bunch of time showing off, saying "oh look, can find a function whose derivative is this, and a function whose derivative is that" when the truth is that if you pick a function out of a hat the probability you can find a nice closed for for the anti derivative is zero!

    • one year ago
  21. Dido525
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    I mean I got the correct answer. But isn't there an easier way to do this?

    • one year ago
  22. satellite73
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    nope you can see that by how annoying your answer is

    • one year ago
  23. Dido525
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    Damn it. Thanks anyways guys :)

    • one year ago
  24. TuringTest
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    haha, true that. PF is just plain annoying

    • one year ago
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