What is laplacetransform t-4(t^2)/2 ?

The answer to laplacetransform t-4(t^2)/2 is 1/(s^2)-4/(s^3)

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laplacetransform t-4(t^2)/2

laplace transform

t - 4 \frac{t ^{2}}{2}

\frac{1}{s ^{2}} - \frac{4}{s ^{3}}

Solution steps

L {t - 4 \cdot \frac{t ^{2}}{2}}

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} - 4 \cdot \frac{1}{2} L {t^{2}}

L {t} : \frac{1}{s ^{2}}

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

= \frac{1}{s ^{2}} - 4 \cdot \frac{1}{2} \cdot \frac{2}{s ^{3}}

Refine

\frac{1}{s ^{2}} - 4 \frac{1}{2} \frac{2}{s ^{3}} : \frac{1}{s ^{2}} - \frac{4}{s ^{3}}

= \frac{1}{s ^{2}} - \frac{4}{s ^{3}}

\int (\frac{1}{x} - \frac{3}{4 x ^{2} + 1}) d x

\frac{d}{d x} (e^{\frac{y}{x}})

\frac{2}{x} - x^{2} + 1

\frac{x ^{2}}{x + 4}

(\frac{b}{a + z ^{2}})^{4}

What is laplacetransform t-4(t^2)/2 ?
The answer to laplacetransform t-4(t^2)/2 is 1/(s^2)-4/(s^3)