I am trying to integrate these functions in as inverse Fourier Transforms, where $q$ is the Fourier variable.

$\int_{-\infty}^{\infty}{\frac{d^3q}{(2\pi)^3}e^{iq\cdot r}\frac{\delta_{ij}}{q^2}} + \int_{-\infty}^{\infty}{\frac{d^3q}{(2\pi)^3}e^{iq\cdot r}\frac{q_i q_j}{q^4}}$

As you see, the indices $i$ and $j$ denote generalized coordinate vectors. Once the transform is performed, I should have a function in terms of $r, r_i, r_j$ (real space), with the Kronecker delta $\delta_{ij}$ still intact.

Being new to Mathematica--is this type of integration implementable straightforwardly? I am comfortable integrating functions without indices, but am not sure how to proceed with the inclusion of the $i$ and $j$ notation.


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