anonymous one year ago laplace transform of t^3.e^4t

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1. IrishBoy123

$$\mathcal L \{t^3.e^{4t}\}$$ = $$\int_{0}^{\infty} t^3 \ e^{4t} \ e^{-st} dt = \int_{0}^{\infty} t^3 \ e^{-(s-4)t} dt = \int_{0}^{\infty} t^3 \ e^{-pt} dt = 3!/p^4 = ???$$, remembering that p = s-4. otherwise, look up the first shifting theorem for Laplace Transforms. it is always in the tables (i think).