What is laplacetransform tsin(t) ?

The answer to laplacetransform tsin(t) is (2s)/((s^2+1)^2)

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laplacetransform tsin(t)

laplace transform

t sin (t)

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

Solution steps

L {t sin (t)}

Use Laplace Transform table:

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

For

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

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

L {sin (t)} : \frac{1}{s ^{2} + 1}

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

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

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

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

\int_{0}^{\infty} x^{2} d x

\int \frac{1}{x ^{2} + 7} d x

\frac{d}{d x} (arctan (x) + \frac{x}{1 + x ^{2}})

(tan (x)) (x)

What is laplacetransform tsin(t) ?
The answer to laplacetransform tsin(t) is (2s)/((s^2+1)^2)