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mony01

  • 2 years ago

anybody know how to do this integral?

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  1. mony01
    • 2 years ago
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    \[\int\limits \frac{ x ^{2} +1}{ (x-3)(x-2)^{2} }dx\]

  2. myininaya
    • 2 years ago
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    you can try partial fractions

  3. mony01
    • 2 years ago
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    im stuck in the part where you have to find A,B, and C

  4. myininaya
    • 2 years ago
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    Can I see what you have so far?

  5. mony01
    • 2 years ago
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    x^2+1=A(x-2)^2+B(x-2)(x-3)+C(x-3)

  6. myininaya
    • 2 years ago
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    You can find C pretty fast by letting x be 2

  7. myininaya
    • 2 years ago
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    You can find A pretty fast also by letting x be 3

  8. myininaya
    • 2 years ago
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    You have two unknown values which it leaves you with the one, B. You can replace A with whatever you found and replace C with whatever you found and then use any value for x besides 2 or 3 to find B

  9. mony01
    • 2 years ago
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    is C=-5 and A=10

  10. myininaya
    • 2 years ago
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    yep

  11. mony01
    • 2 years ago
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    B=-9 when x=1

  12. myininaya
    • 2 years ago
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    yep

  13. mony01
    • 2 years ago
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    when putting it all together how can i simplify -5/(x-2)^2?

  14. myininaya
    • 2 years ago
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    You mean integrate it?

  15. myininaya
    • 2 years ago
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    how would you integrate -5/u^2 with respect to u?

  16. mony01
    • 2 years ago
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    yea

  17. hartnn
    • 2 years ago
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    where are you stuck now?

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