Inverse fourier transform

Hello everyone!

I'm trying to IFT this fraction after I couldn't find it in a Fourier couples table.

$\displaystyle F(j\omega)=\frac{250\pi \delta(\omega)}{30+125\omega}$.

When I integrated the latter, I got: $\displaystyle \frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30+125\omega}e^{-j\omega t}d\omega$ $\displaystyle \ =\frac{1}{2\pi}\int_{0-}^{0+} \frac{250\pi \delta(\omega)}{30}d\omega$ $\displaystyle =\frac{25}{6} u(t)$??

Is there ever a $\displaystyle u(t)$ in IFT ??

Thanks for any help!