What is laplacetransform (t^3e^{-,\at}) ?

The answer to laplacetransform (t^3e^{-,\at}) is e^{-,\at} 6/(s^4)

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laplacetransform (t^3e^{-,\at})

laplace transform

(t^{3} e^{-, at})

e^{-, at} \frac{6}{s ^{4}}

Solution steps

L {e^{-, at} 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)}

= e^{-, at} L {t^{3}}

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

= e^{-, at} \frac{6}{s ^{4}}

x \to 3 - lim (\frac{∣ 3 + x ∣}{3 - x})

\frac{\partial}{\partial y} (e^{y} sin (x y))

\int \frac{9 x}{( 2 - x ^{2} ) ^{3}} d x

\frac{\partial}{\partial x} (x^{3} sin (x y))

\int (1 - e^{- 10 t} - 10 t e^{- 10 t}) d t

What is laplacetransform (t^3e^{-,\at}) ?
The answer to laplacetransform (t^3e^{-,\at}) is e^{-,\at} 6/(s^4)