Residue Theorem

[rubba61]

I am having trouble evaluting the integral from -inf to inf of x*sin(x)/(1+x^4) using residues and closed contour integration in the complex plane. I know how to find the residues of 1/1+z^4 and that I only need to use two of them to represent the two poles in the upper half of the complex plane. However I get a bit confused with the sin and x terms in the numerator. Any ideas about those residues and how they would interact with the residues of the denominator or if the residues of the denominator even have to be considered would be helpful.