$$\int\_0^{\infty} \frac{dx}{1+x^3}$$

So far I have found the indefinite integral, which is:

$$-\frac{1}{6} \ln |x^2-x+1|+\frac{1}{\sqrt{3}} \arctan\left(\frac{2x-1}{\sqrt{3}}\right)+\frac{1}{3}\ln|x+1|$$

Now what do I need to do in order to calculate the improper integral?