Integrating by partial fraction.

[azatkgz]

Homework Statement

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

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.

 

[Dick]

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

 

[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)}

 

[Dick]

That looks ok to me.

 

[rocomath]

damn this prob is going to be long