What is laplacetransform x*e^{(-4x)} ?

The answer to laplacetransform x*e^{(-4x)} is 1/((s+4)^2)

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laplacetransform x*e^{(-4x)}

laplace transform

x \cdot e^{(- 4 x)}

\frac{1}{( s + 4 ) ^{2}}

Solution steps

L {e^{(- 4 x)} x}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

x e^{- 4 x} : f (x) = e^{- 4 x}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{- 4 x}})

L {e^{- 4 x}} : \frac{1}{s + 4}

\frac{d}{d s} (\frac{1}{s + 4}) = - \frac{1}{( s + 4 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s + 4 ) ^{2}})

= \frac{1}{( s + 4 ) ^{2}}

(- 7.2) (9.6)

\int_{1}^{2} \frac{4}{x ^{3} + 4 x} d x

\frac{d}{d x} (csc (8 x))

\int csc (\frac{a x}{b}) \cdot cot (\frac{a x}{b}) d x

f (x) = 4 x - 3

What is laplacetransform x*e^{(-4x)} ?
The answer to laplacetransform x*e^{(-4x)} is 1/((s+4)^2)