What is laplacetransform f(t)=t^2e^{3t} ?

The answer to laplacetransform f(t)=t^2e^{3t} is 2/((s-3)^3)

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laplacetransform f(t)=t^2e^{3t}

laplace transform

f (t) = t^{2} e^{3 t}

\frac{2}{( s - 3 ) ^{3}}

Solution steps

L {e^{3 t} t^{2}}

Use Laplace Transform table:

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

For

t^{2} e^{3 t} : f (t) = e^{3 t}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{3 t}})

L {e^{3 t}} : \frac{1}{s - 3}

\frac{d ^{2}}{d s ^{2}} (\frac{1}{s - 3}) = \frac{2}{( s - 3 ) ^{3}}

= (- 1)^{2} \frac{2}{( s - 3 ) ^{3}}

= \frac{2}{( s - 3 ) ^{3}}

\frac{d}{d x} (\frac{2 x + 3}{x + 2})

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

\int \frac{1}{( 1 + cos ( x ) ) ^{2}} d x

\int \frac{1}{t + 2} d t

\int_{- 1}^{2} x^{2} e^{x^{3} + 1} d x

What is laplacetransform f(t)=t^2e^{3t} ?
The answer to laplacetransform f(t)=t^2e^{3t} is 2/((s-3)^3)