What is laplacetransform 3t^3-2t^2-7t+2 ?

The answer to laplacetransform 3t^3-2t^2-7t+2 is (18)/(s^4)-4/(s^3)-7/(s^2)+2/s

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laplacetransform 3t^3-2t^2-7t+2

laplace transform

3 t^{3} - 2 t^{2} - 7 t + 2

\frac{18}{s ^{4}} - \frac{4}{s ^{3}} - \frac{7}{s ^{2}} + \frac{2}{s}

Solution steps

L {3 t^{3} - 2 t^{2} - 7 t + 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)}

= 3 L {t^{3}} - 2 L {t^{2}} - 7 L {t} + L {2}

L {t^{3}} : \frac{6}{s ^{4}}

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

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

L {2} : \frac{2}{s}

= 3 \cdot \frac{6}{s ^{4}} - 2 \cdot \frac{2}{s ^{3}} - 7 \cdot \frac{1}{s ^{2}} + \frac{2}{s}

Refine

3 \frac{6}{s ^{4}} - 2 \frac{2}{s ^{3}} - 7 \frac{1}{s ^{2}} + \frac{2}{s} : \frac{18}{s ^{4}} - \frac{4}{s ^{3}} - \frac{7}{s ^{2}} + \frac{2}{s}

= \frac{18}{s ^{4}} - \frac{4}{s ^{3}} - \frac{7}{s ^{2}} + \frac{2}{s}

\frac{\partial}{\partial x} (1^{x})

\frac{( x ^{2} + 11 )}{x ^{3}}

(x^{''} + 4 x)^{^{'}}

x \to 0 + lim (\frac{x ^{2}}{2} - \frac{1}{x})

f (x) = 24 x - 4 x

What is laplacetransform 3t^3-2t^2-7t+2 ?
The answer to laplacetransform 3t^3-2t^2-7t+2 is (18)/(s^4)-4/(s^3)-7/(s^2)+2/s