Integrating by partial fraction.

1. Oct 17, 2007

azatkgz

1. The problem statement, all variables and given/known data

$$\int \frac{dx}{(x+1)(x^2+1)(x^3+1)}$$

3. The attempt at a solution

I tried to solve it in 3 ways.
1)$$\frac{A}{(x+1)}+\frac{B}{(x^2+1)}+\frac{C}{(x^3+1)}$$

2)$$\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex}{(x^3+1)}$$

3)$$\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex+Fx^2}{(x^3+1)}$$
But it gives me nonsense.

2. Oct 17, 2007

Dick

(x+1) divides (x^3+1). You can write the partial fraction with just linear and quadratic denominators.

3. Oct 17, 2007

azatkgz

Then should I solve in this way?

$$\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C}{(x+1)^2}+\frac{F+Ex}{(x^2-x+1)}$$

4. Oct 17, 2007

Dick

That looks ok to me.

5. Oct 17, 2007

rocomath

damn this prob is gonna be long