What is laplacetransform 3t^4e^{-2t} ?

The answer to laplacetransform 3t^4e^{-2t} is (72)/((s+2)^5)

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laplacetransform 3t^4e^{-2t}

laplace transform

3 t^{4} e^{- 2 t}

\frac{72}{( s + 2 ) ^{5}}

Solution steps

L {3 e^{- 2 t} t^{4}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 3 L {t^{4} e^{- 2 t}}

L {t^{4} e^{- 2 t}} : \frac{24}{( s + 2 ) ^{5}}

= 3 \cdot \frac{24}{( s + 2 ) ^{5}}

Refine

3 \frac{24}{( s + 2 ) ^{5}} : \frac{72}{( s + 2 ) ^{5}}

= \frac{72}{( s + 2 ) ^{5}}

x^{5}, e^{3} x^{2}

\frac{2 s - 3}{s ^{2} + 4}

y^{^{'}} + x y = 1 x y^{3}

\int_{1}^{6} - x^{2} + 7 x - 6 d x

x \to 2 + lim (\frac{6 x}{x - 2})

What is laplacetransform 3t^4e^{-2t} ?
The answer to laplacetransform 3t^4e^{-2t} is (72)/((s+2)^5)