Question

Integration by Partial fractions question

Answer 1

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

Answer 2

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?

Answer 3

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.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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 \[\frac{ x+3}{ x ^{2}-1 }\]

Answer 8

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

Answer 9

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!

Answer 10

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

Answer 11

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