What is laplacetransform 6t^3e^{-2t} ?

The answer to laplacetransform 6t^3e^{-2t} is (36)/((s+2)^4)

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laplacetransform 6t^3e^{-2t}

laplace transform

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

\frac{36}{( s + 2 ) ^{4}}

Solution steps

L {6 e^{- 2 t} t^{3}}

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)}

= 6 L {t^{3} e^{- 2 t}}

L {t^{3} e^{- 2 t}} : \frac{6}{( s + 2 ) ^{4}}

= 6 \cdot \frac{6}{( s + 2 ) ^{4}}

Refine

6 \frac{6}{( s + 2 ) ^{4}} : \frac{36}{( s + 2 ) ^{4}}

= \frac{36}{( s + 2 ) ^{4}}

\int \frac{1}{( 1 + 4 x ^{2} ) ( arctan ( 2 x ) ) ^{3}} d x

\int sin^{4} (6 x) d x

x \to 0 + lim (3 x^{x})

2 x^{2} y^{^{''}} + 6 x y^{^{'}} + 2 y = 0, y (1) = 2, y^{^{'}} (1) = - 1

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 t e^{3 t}

What is laplacetransform 6t^3e^{-2t} ?
The answer to laplacetransform 6t^3e^{-2t} is (36)/((s+2)^4)