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:<math>\begin{align}
\int \frac{d^3 k}{(2\pi)^3} \left(\mathbf{\hat k}\cdot \mathbf{\hat r}\right)^2 \frac{\exp \left (i\mathbf{k}\cdot \mathbf{r}\right )}{k^2 +m^2} &= \int_0^{\infty} \frac{k^2 dk}{(2\pi)^2} \int_{-1}^{1} du \ u^2 \frac{e^{ikru}}{k^2 + m^2} \\
&= 2 \int_0^{\infty} \frac{k^2 dk}{(2\pi)^2} \frac{1}{k^2 + m^2} \left\{\frac{1}{kr} \sin(kr) + \frac{2}{(kr)^2} \cos(kr)- \frac{2}{(kr)^3} \sin(kr) \right \} \\
&= \frac{e^{-mr}}{4\pi r} \left\{1 + \frac{2}{mr} - \frac{2}{(mr)^2} \left(e^{mr}-1 \right) \right \}
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