Question

Please help with an inverse Laplace Transform!

Answer 1

\[\frac{ 1 }{ (s-1)^{4} }\]

Answer 2

\[e^t \frac{t^3}{6}\]

Answer 3

thank you! How did you work it out please?

Answer 4

let p = s-1

so you are looking for \[\mathcal{L}^{-1} \left\{ \frac{1}{p^4} \right\}\]

which is\[\int\limits\limits_{0}^{\infty} \frac {t^3}{6} \ e^{-pt} dt \] \[\int\limits_{0}^{\infty} \frac {t^3}{6} e^{-(s-1)t} dt \]
\[\int\limits\limits_{0}^{\infty} e^{t} \ \frac {t ^{3}}{6} \ e^{-st} dt \]

Answer 5

Ah ok thank you!!