Mathematics

Take the following Fourier transform conventions $$ \tilde{f}(\mathbf{p}) =\int f(\mathbf{x}) \ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x $$ $$ f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\ e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}. $$ In physics, it is useful to compute the transform of $1/p^3$ $$ I=\int \frac{1}{p^3}\ e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}. $$ But I have no idea what it even mean since the integral is not well-defined.

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The Fourier transform of $1/p^3$

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