What is laplacetransform t^2cos(t) ?

The answer to laplacetransform t^2cos(t) is -(2s(-s^2+3))/((s^2+1)^3)

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laplacetransform t^2cos(t)

laplace transform

t^{2} cos (t)

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

Solution steps

L {t^{2} cos (t)}

Use Laplace Transform table:

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

For

t^{2} cos (t) : f (t) = cos (t), k = 2

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

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

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

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = t + e^{2 t}

f (x) = 9 x^{2}

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 d x

\frac{d y}{d x} + 7 x e^{y} = 0

\frac{d}{d x} (lo g_{4} (sec (x)))

What is laplacetransform t^2cos(t) ?
The answer to laplacetransform t^2cos(t) is -(2s(-s^2+3))/((s^2+1)^3)