How can I calculate the following integral:
$\int_{0}^{\infty}\frac{x^{4} + 1}{x^{4} - 1}\cdot \frac{\sin(x)}{2x} dx$
I tried separating it on two domains:
a) 0 to 1 which holds x = 0 as a simple pole and also observed that it is even.
b) 1 to infinity, in which i can't seem to find any pole.
Any help would be appreciated.