What is laplacetransform t^2+e^{-2t}sin(3t) ?

The answer to laplacetransform t^2+e^{-2t}sin(3t) is 2/(s^3)+3/((s+2)^2+9)

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laplacetransform t^2+e^{-2t}sin(3t)

laplace transform

t^{2} + e^{- 2 t} sin (3 t)

\frac{2}{s ^{3}} + \frac{3}{( s + 2 ) ^{2} + 9}

Solution steps

L {t^{2} + e^{- 2 t} sin (3 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} + L {e^{- 2 t} sin (3 t)}

L {t^{2}} : \frac{2}{s ^{3}}

L {e^{- 2 t} sin (3 t)} : \frac{3}{( s + 2 ) ^{2} + 9}

= \frac{2}{s ^{3}} + \frac{3}{( s + 2 ) ^{2} + 9}

x \to - 1 lim (3 x^{3} + 2 x^{2} + 3)

x \to 0 + lim (e^{(\frac{1}{x})})

\frac{y ^{2} - 2}{2 y ^{2}}

\int \frac{x ^{3} - 2 x ^{2} + 1}{x - 3} d x

\int_{1}^{2} \frac{( ln ( x ) ) ^{2}}{x} d x

What is laplacetransform t^2+e^{-2t}sin(3t) ?
The answer to laplacetransform t^2+e^{-2t}sin(3t) is 2/(s^3)+3/((s+2)^2+9)