Question

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

Answer 1

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

Answer 2

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

Answer 3

oops forgot a dx there

Answer 4

do u want answer or explanation

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

i m lost

Answer 9

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

Answer 10

first factor the function

Answer 11

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

Answer 12

yes that is true

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

Yah that looks right :)