anonymous 3 years ago Evaluate the integral. The integral will be entered below. The title of this section is Intergration of Rational Fractions by Partial Fractions

1. anonymous

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

2. anonymous

I can simplify it down to $\int\limits_{}^{}\frac{ A }{ x }+\frac{ B }{ x-1 }+\frac{ C }{ x+1 }$ but get lost when solving for A, B and C

3. anonymous

oops forgot a dx there

4. anonymous

do u want answer or explanation

5. anonymous

explanation my math teacher was very confusing when going over this section (thick accent)

6. anonymous

I probably screwed up because its three terms now instead of two

7. anonymous

I had $x^2+2x-1=Ax+B(x-1)+C(x+1)$ which is obviously wrong

8. anonymous

i m lost

9. anonymous

yea this method is past l'Hopital's rule which I think you said you did not know earlier so it might be a little higher than your current level of math course

10. anonymous

first factor the function

11. anonymous

which I did getting x(x-1)(x+1) on the bottom

12. anonymous

yes that is true

13. zepdrix

$\large \frac{x^2+2x-1}{x(x-1)(x+1)} \qquad =\qquad \frac{A}{x}+\frac{B}{x-1}+\frac{C}{x+1}$You should set it up like this. It looks like you're on the right track. You just didn't multiply through correctly.

14. zepdrix

Multiply both sides by the denominator on the left. :O

15. anonymous

O GOD top ten list of signs I need to go to bed

16. anonymous

so the correct answer is $x^2+2x-1=A(x+1)(x-1)+Bx(x+1)+Cx(x-1)$$=(A+B+C)X^2+(B-C)X-A$$A=1, B=1, C=-1$

17. zepdrix

Yah that looks right :)