How to evaluate $\int _{-\infty }^{\infty }\!{\frac {\cos \left( x \right) }{{x}^{4}+1}}{dx}$ How to evaluate the following integral?
$$
\int _{-\infty }^{\infty }\!{\frac {\cos \left( x \right) }{{x}^{4}+1}}{dx}
$$
Unlike this example, according to maple, the solution does not contain sine and cosine integrals. But how does it eavluate this kind of integrals? The method?

This can be done using residues, with the function $f(z) = \exp(i z)/(z^4 + 1)$
and a contour that goes along the real axis and returns on a circular arc in the upper half plane.  
