Finding the convergence of an integral

I'm trying to solve the following integral:

$\displaystyle \int^{\infty}_{0}\frac{x^{3}}{x^{6}+1}dx$

I know that it converges, but I am having trouble evaluating it. I've tried partial fractions, any u sub I can think of, and nothing seems to quite work...

Re: Finding the convergence of an integral

Read about using residues to compute improper integrals of real functions.

here for example.

Re: Finding the convergence of an integral

Very interesting stuff thank you!