How do I integrate the improper integral $$\int\_{-\infty}^{\infty} \frac{dx}{1+x^{12}}$$ using partial fraction decomposition?

I am restricted to use only the principles taught in Calculus 2, which entails partial fraction decomposition. I have tried factoring the denominator but was quickly stumped at the complicated roots. I am unsure of how to proceed. I even thought of looking at it as a series but I don't think I can do that.

Thank you very much for your help. I greatly appreciate it.