I need to calculate the integration using Cauchy's Residue Theorem $$\int_{-\infty}^{\infty} \frac{x^2}{(x^2+1)(x^2+9)}dx$$
I am stuck here how can I approach this.
$$\int_{Cr}^{} f(z) dz = 0$$.
I need to show that the function is zero using Jordan's Lemma.