anonymous
  • anonymous
Integration by Partial fractions question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits\limits\limits\limits_{}^{}\frac{ x ^{2}+x+2 }{ x ^{2}-1 } dx \]
anonymous
  • anonymous
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?
anonymous
  • anonymous
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.

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anonymous
  • anonymous
No. I immediately used partial fraction. Then I need to divide this first?
anonymous
  • anonymous
yes. you'll miss a few terms if u didn't(faced this problem once in my exam==costed me 5 precious minutes)
anonymous
  • anonymous
Oh. Ok, I'll try dividing it first.
anonymous
  • anonymous
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 \[\frac{ x+3}{ x ^{2}-1 }\]
anonymous
  • anonymous
yeah. then proceed to partial frac it. then, after that you can integrate it.
anonymous
  • anonymous
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!
anonymous
  • anonymous
\(\int (1+\frac{x+3}{x^2 -1})dx \) .<--this yup. You're welcome :)
anonymous
  • anonymous
Oh, I ignored the 1. Thank you very much again! :D

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