use residue calculus to evaluate?

Question

integral from -inf to inf of (x*sin(x)) / ((x^4)+1) dx

Answer 1

Well, what are the poles in the upper half plane? I see two of them, both on the unit circle, one at 45 degrees and one at 135 degrees. Evaluate the numerator at those poles, add up the results, multiply by 2 * pi * i, and you'll have your answer.