Fourier antitransform using scaling property?

Question

I'm trying to calculate the antitransform of:

$\frac{1}{2\cdot(1+5w)^2}$

Now I know the antitransform of $\frac{1}{(1+5w)^2} = t \cdot e^{-5t} u(t) $

But in this case I got that divided by 2. I assumed I had to use the scaling property which says:

$F[f(ax)] = \frac{1}{|a|} \hat{f}(\frac{w}{a})$

Now I'm not really sure how to apply this. Could anyone help?

Answer 1

If $h(t)$ is the inverse Fourier transform of $H(\omega)$, then by linearity the inverse Fourier transform of $aH(\omega)$ is simply $ah(t)$. This has nothing to do with the scaling property you mentioned, because the latter refers to the scaling of the argument of the function.