$$\int\_{-\infty}^{\infty} \frac{dx}{(x^2+1)^2(x^2+16)}$$

**My attempt:**

We are integrating over the real axis, which is the real part of a set of complex numbers, so
$$=\int\_{-\infty}^{\infty} \frac{dz}{(z^2+1)^2(z^2+16)}$$

$$=\int\_{-\infty}^{\infty} \frac{dz}{((z+i)(z-i))^2(z+4i)(z-4i)}$$

But I notice that all of the singularities are imaginary! Should this give me pause? What should I do now?