## whatisthequestion Group Title Evaluate the integral. The integral will be entered below. The title of this section is Intergration of Rational Fractions by Partial Fractions one year ago one year ago

1. whatisthequestion Group Title

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

2. whatisthequestion Group Title

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. whatisthequestion Group Title

oops forgot a dx there

4. Best_Mathematician Group Title

do u want answer or explanation

5. whatisthequestion Group Title

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

6. whatisthequestion Group Title

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

7. whatisthequestion Group Title

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

8. Best_Mathematician Group Title

i m lost

9. whatisthequestion Group Title

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. Best_Mathematician Group Title

first factor the function

11. whatisthequestion Group Title

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

12. Best_Mathematician Group Title

yes that is true

13. zepdrix Group Title

$\large \frac{x^2+2x-1}{x(x-1)(x+1)} \qquad =\qquad \frac{A}{x}+\frac{B}{x-1}+\frac{C}{x+1}$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 Group Title

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

15. whatisthequestion Group Title

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

16. whatisthequestion Group Title

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 Group Title

Yah that looks right :)