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Dido525

  • 2 years ago

Evaluate the Intergal

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

  2. Dido525
    • 2 years ago
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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.

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

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

  5. DHASHNI
    • 2 years ago
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    it is jus to simplify the question

  6. Dido525
    • 2 years ago
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    Hmm Okay... Let me see...

  7. calmat01
    • 2 years ago
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    Yep. it simplifies, reducing your amount of work.

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

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

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

  11. DHASHNI
    • 2 years ago
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    yeah ^ he's right

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

  13. satellite73
    • 2 years ago
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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

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

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

  16. satellite73
    • 2 years ago
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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

  17. Dido525
    • 2 years ago
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    Wolfram made I think... 9 substitutions. I refuse to do that.

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

  19. satellite73
    • 2 years ago
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    art who?

  20. satellite73
    • 2 years ago
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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!

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

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

  23. Dido525
    • 2 years ago
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    Damn it. Thanks anyways guys :)

  24. TuringTest
    • 2 years ago
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    haha, true that. PF is just plain annoying

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