What is laplacetransform xsin(3x) ?

The answer to laplacetransform xsin(3x) is (6s)/((s^2+9)^2)

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laplacetransform xsin(3x)

laplace transform

x sin (3 x)

\frac{6 s}{( s ^{2} + 9 ) ^{2}}

Solution steps

L {x sin (3 x)}

Use Laplace Transform table:

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

For

x sin (3 x) : f (x) = sin (3 x), k = 1

= (- 1)^{1} \frac{d}{d s} (L {sin (3 x)})

L {sin (3 x)} : \frac{3}{s ^{2} + 9}

\frac{d}{d s} (\frac{3}{s ^{2} + 9}) = - \frac{6 s}{( s ^{2} + 9 ) ^{2}}

= (- 1)^{1} (- \frac{6 s}{( s ^{2} + 9 ) ^{2}})

= \frac{6 s}{( s ^{2} + 9 ) ^{2}}

\frac{d}{d x} (\frac{1}{e ^{x} + 1})

x \cdot ln (x)

\int \frac{x + 1}{x ^{3}} d x

\frac{d}{d x} (x e^{8 x})

n = 0 \sum \infty 4^{2 n + 1}

What is laplacetransform xsin(3x) ?
The answer to laplacetransform xsin(3x) is (6s)/((s^2+9)^2)