What is laplacetransform 10t^3e^{-2t} ?

The answer to laplacetransform 10t^3e^{-2t} is (60)/((s+2)^4)

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laplacetransform 10t^3e^{-2t}

laplace transform

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

\frac{60}{( s + 2 ) ^{4}}

Solution steps

L {10 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)}

= 10 L {t^{3} e^{- 2 t}}

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

= 10 \cdot \frac{6}{( s + 2 ) ^{4}}

Refine

10 \frac{6}{( s + 2 ) ^{4}} : \frac{60}{( s + 2 ) ^{4}}

= \frac{60}{( s + 2 ) ^{4}}

y = \frac{1}{2} x^{3} + 2, y = x + 1, 0, 2

f (x) = x^{2} + x, (- 2, 2)

\int_{3}^{7} \frac{1}{6 x + 7} d x

\frac{\partial}{\partial u} (\frac{v}{u - v})

\frac{d y}{d x} = 2 sin (x) (y - 3)

What is laplacetransform 10t^3e^{-2t} ?
The answer to laplacetransform 10t^3e^{-2t} is (60)/((s+2)^4)