How do I solve a Partial Fraction Problem?

[jdawg]

Homework Statement

∫(5x²+20x+6)/(x³+2x²+x

Homework Equations

The Attempt at a Solution

(5x²+20x+6)/(x³+(x(x²+2x+1)

(5x²+20x+6)=(A/x)+(B/(x+1))+(C/(x+1))

(5x²+20x+6)=x²(A+B+C)+x(2A+B+C)+A

5=A+B+C
20=2A+B+C
6=A

It's not coming out quite right. Did I maybe factor the denominator incorrectly?

 

[LCKurtz]

Homework Statement

∫(5x²+20x+6)/(x³+2x²+x

Homework Equations

The Attempt at a Solution

(5x²+20x+6)/(x³+(x(x²+2x+1)

(5x²+20x+6)=(A/x)+(B/(x+1))+(C/(x+1))

You want$$
\frac{5x^2+20x+6}{x(x+1)^2}=\frac A x + \frac{Bx+C}{(x+1)^2}$$

 

[jdawg]

Ohh! But wouldn't you need one for x+1?:

A/x + (Bx+C)/(x+1)² + (Dx+E)/(x+1)

 

[Dick]

Ohh! But wouldn't you need one for x+1?:

A/x + (Bx+C)/(x+1)² + (Dx+E)/(x+1)

No, you only need three independent variables. You could write it as $$\frac A x + \frac{Bx+C}{(x+1)^2}$$ as LCKurtz did, or you could write it as $$\frac A x + \frac{B}{(x+1)^2}+\frac{C}{(x+1)}$$.

 

[jdawg]

Oh ok! Thanks for clearing that up :)