What is laplacetransform tsin(3t) ?

The answer to laplacetransform tsin(3t) is (6s)/((s^2+9)^2)

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laplacetransform tsin(3t)

laplace transform

t sin (3 t)

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

Solution steps

L {t sin (3 t)}

Use Laplace Transform table:

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

For

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

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

L {sin (3 t)} : \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}}

\int (x^{10} - 5 x^{2})^{3} (x^{9} - x) d x

x y^{^{'}} + 2 y - 12 = 0

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

x \to 0 lim (x cos (\frac{1}{x}))

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