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taiga_aisaka
 2 years ago
Integration by Partial fractions question
taiga_aisaka
 2 years ago
Integration by Partial fractions question

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taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits\limits\limits\limits_{}^{}\frac{ x ^{2}+x+2 }{ x ^{2}1 } dx \]

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0Whenever I solve this I always get: A= 1 B= 2 then \[\int\limits\limits_{}^{} \frac{ 1 }{ x+1 } + \frac{ 2 }{ x1 } dx\] 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?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1did you do the long division first before u partial frac'ed it? u'll lose a few terms if you didn't do that.

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0No. I immediately used partial fraction. Then I need to divide this first?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1yes. you'll miss a few terms if u didn't(faced this problem once in my exam==costed me 5 precious minutes)

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0Oh. Ok, I'll try dividing it first.

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0This 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 \[\frac{ x+3}{ x ^{2}1 }\]

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1yeah. then proceed to partial frac it. then, after that you can integrate it.

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0Just 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!

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1\(\int (1+\frac{x+3}{x^2 1})dx \) .<this yup. You're welcome :)

taiga_aisaka
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, I ignored the 1. Thank you very much again! :D
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