What is laplacetransform x*e^x ?

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

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laplacetransform x*e^x

laplace transform

x \cdot e^{x}

\frac{1}{( s - 1 ) ^{2}}

Solution steps

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

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

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

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

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

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

\frac{d}{d t} (cos (120 π) t)

\int_{0}^{l} sin^{2} (\frac{nπ x}{l}) d x

\int cos (1 - x) d x

\frac{d}{d x} (\frac{2}{( 1 - x ) ^{2}})

\int \frac{x ^{3} - 2}{x ^{2} + 3 x + 2} d x

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