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taiga_aisaka

  • 3 years ago

Integration by Partial fractions question

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

  2. taiga_aisaka
    • 3 years ago
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    Whenever I solve this I always get: A= -1 B= 2 then \[\int\limits\limits_{}^{} -\frac{ 1 }{ x+1 } + \frac{ 2 }{ x-1 } dx\] after substituting A and B and checking if I will still get the original integral, it's not the same anymore. How can I solve this integral?

  3. Shadowys
    • 3 years ago
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    did you do the long division first before u partial frac'ed it? u'll lose a few terms if you didn't do that.

  4. taiga_aisaka
    • 3 years ago
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    No. I immediately used partial fraction. Then I need to divide this first?

  5. Shadowys
    • 3 years ago
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    yes. you'll miss a few terms if u didn't(faced this problem once in my exam==costed me 5 precious minutes)

  6. taiga_aisaka
    • 3 years ago
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    Oh. Ok, I'll try dividing it first.

  7. taiga_aisaka
    • 3 years ago
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    This is a bit embarrassing, but I'm not sure if I got the quotient right. When I divide the two I get the answer of 1 with a remainder of \[\frac{ x+3}{ x ^{2}-1 }\]

  8. Shadowys
    • 3 years ago
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    yeah. then proceed to partial frac it. then, after that you can integrate it.

  9. taiga_aisaka
    • 3 years ago
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    Just to be clear, after dividing I will get this? \[\int\limits_{}^{} \frac{ x+3 }{ x ^{2}-1 }\] I will then proceed to partial fraction then integrate? Thanks!

  10. Shadowys
    • 3 years ago
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    \(\int (1+\frac{x+3}{x^2 -1})dx \) .<--this yup. You're welcome :)

  11. taiga_aisaka
    • 3 years ago
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    Oh, I ignored the 1. Thank you very much again! :D

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