# Homework Help: Partial Frac. Decomp. Integral ( long div? )

1. Oct 26, 2011

### theRukus

1. The problem statement, all variables and given/known data
\int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx

2. Relevant equations

3. The attempt at a solution
I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that the polynomial has no factors...? I'm confused, can someone give me a push in the right direction?

Thanks PhysicsForums!

2. Oct 26, 2011

### vela

Staff Emeritus
The division ends when the degree of the remainder is less than the degree of the divisor. In this case, when the remainder is of the form Cx+D, you're done. The result of your division will be that
$$\frac{-3x^3+12x+30}{x^2-x-6} = Ax + B + \frac{Cx+D}{x^2-x-6}$$

3. Oct 26, 2011

### Staff: Mentor

The long division does come to an end. You should have gotten -3x - 3 + <remainder>/(x2 - x - 6).

What I'm calling <remainder> is a first-degree polynomial.

4. Oct 26, 2011

### theRukus

Got it! Thanks guys, I owe an infinite amount of thanks to PhysicsForums..!