I was asked to write down the Fourier integral of $x^2$ using the following convention:
$$\begin{align*} \text{Fourier transform}\quad&\hat{f}(k) = \dfrac1{2\pi}\int_{-\infty}^{\infty}f(x)\,e^{-ikx}\,\mathrm dx \\ \text{Fourier integral}\quad&f(x) = \int_{-\infty}^{\infty}\hat{f}(k)\,e^{ikx}\,\mathrm dk \end{align*}$$
However the solution has baffled me as it was written as follows: $$ x^2 = -\int_{-\infty}^{\infty}\delta''(k)\,e^{ikx}\,\mathrm dk $$
I have no idea how this is the solution any help would be appreciated.