Partial Fractions integral

[bounce22]

I'm having trouble figuring out how to separate the following integral into partial fractions

int( 1/(x^4+x) dx)

Do i factor out x on the bottom and go from there?
I think that I am supposed to use something with an irreducible quadratic factor, but i'm not sure on how to get to that step.

 

[pka]

I'm having trouble figuring out how to separate the following integral into partial fractions
int( 1/(x^4+x) dx)

Look at this.

 

[galactus]

\(\displaystyle \int\frac{1}{x^{4}+x}dx\)

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

You can make this a wee bit easier by making a sub.

Let \(\displaystyle t=x^{3}, \;\ dx=\frac{1}{3}t^{\frac{-2}{3}}dt\)

This gives \(\displaystyle \frac{1}{3}\int\frac{1}{t(t+1)}dt=\frac{1}{3}\int\frac{1}{t}-\frac{1}{3}\int\frac{1}{t+1}dt\)

Integrate and resub \(\displaystyle t=x^{3}\)