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anonymous

  • 5 years ago

∫x+1/2x-x2+2 dx

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  1. anonymous
    • 5 years ago
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    Pls guys help me solve this problem i have Exams tomorrow. pls

  2. anonymous
    • 5 years ago
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    do you know how to long divide polynomials?

  3. anonymous
    • 5 years ago
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    yes

  4. anonymous
    • 5 years ago
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    That's pretty much what you have to do here, so that your integral becomes (-x+3) - (1/(x+1)). Then you can solve the integral.

  5. anonymous
    • 5 years ago
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    hold up a minute, I think I messed it up, give me a minute or two.

  6. anonymous
    • 5 years ago
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    ok

  7. anonymous
    • 5 years ago
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    the denominator is 2x-x square + 2

  8. anonymous
    • 5 years ago
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    it looks like you separate by partial fractions \[x+1 =( Ax +B)/(2x-x^2+2)\]. Because the deonimator is a irreducible quadratic eq. Once you solve for A and B, then you should have a differentiable eq.

  9. anonymous
    • 5 years ago
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    sorry about the mix up before I jumped into a bad conclusion too fast.

  10. anonymous
    • 5 years ago
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    \[\int\limits \left(2+\frac{1}{2 x}+x-x^2\right) \, dx = 2 x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{\text{Log}[x]}{2} \]

  11. anonymous
    • 5 years ago
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    hello

  12. anonymous
    • 5 years ago
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    is that the final ans.

  13. anonymous
    • 5 years ago
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    from robtobey, Yes. Another version is the result factored: \[\frac{1}{6} \left(12 x+3 x^2-2 x^3+3 \text{Log}[x]\right) \]

  14. anonymous
    • 5 years ago
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    You can check the result of the integration by taking the derivative of the result with respect to x.

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