## taiga_aisaka 2 years ago Integration by Partial fractions question

1. taiga_aisaka

$\int\limits\limits\limits\limits_{}^{}\frac{ x ^{2}+x+2 }{ x ^{2}-1 } dx$

2. taiga_aisaka

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?

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

No. I immediately used partial fraction. Then I need to divide this first?

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

Oh. Ok, I'll try dividing it first.

7. taiga_aisaka

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 $\frac{ x+3}{ x ^{2}-1 }$

yeah. then proceed to partial frac it. then, after that you can integrate it.

9. taiga_aisaka

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!

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

11. taiga_aisaka

Oh, I ignored the 1. Thank you very much again! :D