Laplace transform does not work

Question

I tried to use Laplace transform for this expression using Wolfram Alpha : $3.297\times10^9s^{-2.327}+1480$, but even Wolfram cannot do this... Why ?

Thank you very much !

Answer 1

The Laplace transform of $a s^b + c$ is given by $$ \mathcal{L}_{s \to t}[a s^b + c] = \frac{c}{t} + \frac{a \Gamma(b+1)}{t^{b+1}} $$ where $\Gamma(x)$ is the gamma function, which is a continuous version of the factorial function. You can see by this link that it thinks this is only valid for $\Re(b)>-1$ which your expression doesn't follow. So this might be the reason why it couldn't return an answer.