# Integrating with indices

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.