What is laplacetransform t^2t^3 ?

The answer to laplacetransform t^2t^3 is (120)/(s^6)

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laplacetransform t^2t^3

laplace transform

t^{2} t^{3}

\frac{120}{s ^{6}}

Solution steps

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

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

L {t^{3}} : \frac{6}{s ^{4}}

\frac{d ^{2}}{d s ^{2}} (\frac{6}{s ^{4}}) = \frac{120}{s ^{6}}

= (- 1)^{2} \frac{120}{s ^{6}}

= \frac{120}{s ^{6}}

\int_{0}^{\infty} x e^{- 2 x} d x

\int (- 4 x y + 2 x^{3} - 2 y + 3) d x

\int (sin (wt))^{2} d t

\int (2^{x} + e^{x}) d x

\int_{- 3}^{3} \frac{14}{x ^{2} - 6 x - 40} d x

What is laplacetransform t^2t^3 ?
The answer to laplacetransform t^2t^3 is (120)/(s^6)