What is laplacetransform t^2sin(5t) ?

The answer to laplacetransform t^2sin(5t) is -(10(-3s^2+25))/((s^2+25)^3)

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laplacetransform t^2sin(5t)

laplace transform

t^{2} sin (5 t)

- \frac{10 ( - 3 s ^{2} + 25 )}{( s ^{2} + 25 ) ^{3}}

Solution steps

L {t^{2} 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^{2} sin (5 t) : f (t) = sin (5 t), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {sin (5 t)})

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

\frac{d ^{2}}{d s ^{2}} (\frac{5}{s ^{2} + 25}) = - \frac{10 ( - 3 s ^{2} + 25 )}{( s ^{2} + 25 ) ^{3}}

= (- 1)^{2} (- \frac{10 ( - 3 s ^{2} + 25 )}{( s ^{2} + 25 ) ^{3}})

= - \frac{10 ( - 3 s ^{2} + 25 )}{( s ^{2} + 25 ) ^{3}}

\frac{\partial}{\partial y} (y^{2} + 2)

\int - \frac{1}{e ^{3 x}} d x

\int 5 cos^{3} (5 x) d x

\frac{\partial}{\partial x} (cos^{9} (x^{8} y^{6}))

4^{\frac{c}{x}}

What is laplacetransform t^2sin(5t) ?
The answer to laplacetransform t^2sin(5t) is -(10(-3s^2+25))/((s^2+25)^3)