Question

laplace transform of t^3.e^4t

Answer 1

\( \mathcal L \{t^3.e^{4t}\}\) = \(\int_{0}^{\infty} t^3 \ e^{4t} \ e^{-st} dt = \int_{0}^{\infty} t^3 \ e^{-(s-4)t} dt = \int_{0}^{\infty} t^3 \ e^{-pt} dt = 3!/p^4 = ???\), remembering that p = s-4.

otherwise, look up the first shifting theorem for Laplace Transforms. it is always in the tables (i think).