What is laplacetransform e^{5t}t^3 ?

The answer to laplacetransform e^{5t}t^3 is 6/((s-5)^4)

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laplacetransform e^{5t}t^3

laplace transform

e^{5 t} t^{3}

\frac{6}{( s - 5 ) ^{4}}

Solution steps

L {e^{5 t} t^{3}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

e^{5 t} t^{3} : f (t) = e^{5 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{5 t}})

L {e^{5 t}} : \frac{1}{s - 5}

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s - 5}) = - \frac{6}{( s - 5 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s - 5 ) ^{4}})

= \frac{6}{( s - 5 ) ^{4}}

\int x^{3} x^{2} + 1 d x

\int \frac{e ^{3 x}}{e ^{3 x} + 2} d x

\frac{d}{d x} (\frac{x ^{4} + 3}{6 x})

\frac{d}{d y} (3 y)

\frac{d}{d x} (1 + 2 e^{3 x})

What is laplacetransform e^{5t}t^3 ?
The answer to laplacetransform e^{5t}t^3 is 6/((s-5)^4)