I have to show that the Fourier transform of the function $f(x) = \ln(x)$ is:
$$\mathfrak{F}[\ln(x)](k) = \frac{1}{k}\sqrt{\frac{\pi}{2}} - \frac{1}{|k|}\sqrt{\frac{\pi}{2}} + i\ \sqrt{\frac{\pi^3}{2}} \delta(k) - \gamma\sqrt{2\pi}\ \delta(k)$$
Where $\gamma = $ Euler-Mascheroni constant and $\delta(k)$ = Dirac Delta function.
Any hint for the integration?