What is laplacetransform tsin(5t) ?

The answer to laplacetransform tsin(5t) is (10s)/((s^2+25)^2)

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laplacetransform tsin(5t)

laplace transform

t sin (5 t)

\frac{10 s}{( s ^{2} + 25 ) ^{2}}

Solution steps

L {t sin (5 t)}

Use Laplace Transform table:

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

For

t sin (5 t) : f (t) = sin (5 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {sin (5 t)})

L {sin (5 t)} : \frac{5}{s ^{2} + 25}

\frac{d}{d s} (\frac{5}{s ^{2} + 25}) = - \frac{10 s}{( s ^{2} + 25 ) ^{2}}

= (- 1)^{1} (- \frac{10 s}{( s ^{2} + 25 ) ^{2}})

= \frac{10 s}{( s ^{2} + 25 ) ^{2}}

\int \frac{9 sin ( x )}{cos ^{3} ( x )} d x

x \to 1 lim (x^{\frac{2}{( 1 - x )}})

\int_{0}^{2} (x + 2) d x

\int 20 e^{- 0.8 t} d t

\frac{\partial}{\partial x} (y + 2 - \frac{2}{x})

What is laplacetransform tsin(5t) ?
The answer to laplacetransform tsin(5t) is (10s)/((s^2+25)^2)