I am trying to integrate the following, $$\int d^{3}\vec{k} \frac{\exp(i\vec{k}\cdot\vec{R})}{k^{2}(k^{2}+a^{2})^{2}},$$ where $\vec{R}$ is a constant real vector. The integration is over the full space $0<k<\infty$, $0<\theta<\pi$, $0<\phi<2\pi$.
I have taken $\vec{R}$ along the direction of $z$ axis to simplify the problem. I proceeded as follows: $$\int k^{2}dk \sin\theta d\theta d\phi\frac{\exp(ikR\cos\theta)}{k^{2}(k^{2}+a^{2})^{2}}$$ $d\phi$ integral gives $2\pi$, $$\int dk\int d(-\cos\theta)\frac{\exp(ikR\cos\theta)}{(k^{2}+a^{2})^{2}} $$ $$-\int_{0}^{\infty} dk\int_{0}^{\pi} d(\cos\theta)\frac{\exp(ikR\cos\theta)}{(k^{2}+a^{2})^{2}} $$ $$-\int_{0}^{\infty} dk\int_{1}^{-1} d(\cos\theta)\frac{\exp(ikR\cos\theta)}{(k^{2}+a^{2})^{2}} $$ integrating $\theta$ integral completely we get $$\int_{0}^{\infty} dk \frac{\exp(ikR)-\exp(-ikR)}{ikR(k^{2}+a^{2})^{2}} $$ Rearranging further,$$\frac{1}{iR}\int_{0}^{\infty} dk \frac{\exp(ikR)-\exp(-ikR)}{k(k^{2}+a^{2})^{2}} $$ How do proceed further from here. Can someone help me solving this problem completely to get the final answer?