What is laplacetransform 3t^2-9t ?

The answer to laplacetransform 3t^2-9t is 6/(s^3)-9/(s^2)

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laplacetransform 3t^2-9t

laplace transform

3 t^{2} - 9 t

\frac{6}{s ^{3}} - \frac{9}{s ^{2}}

Solution steps

L {3 t^{2} - 9 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)}

= 3 L {t^{2}} - 9 L {t}

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

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

= 3 \cdot \frac{2}{s ^{3}} - 9 \cdot \frac{1}{s ^{2}}

Refine

3 \frac{2}{s ^{3}} - 9 \frac{1}{s ^{2}} : \frac{6}{s ^{3}} - \frac{9}{s ^{2}}

= \frac{6}{s ^{3}} - \frac{9}{s ^{2}}

(4 x + 5)^{\frac{1}{5}}

arccos (\frac{x}{5})

\int \frac{4 x}{x ^{2} + 5} d x

(x^{2} + x y - y^{2}) d x + x y d y = 0

x \to 0 lim ((x - 3) x)

What is laplacetransform 3t^2-9t ?
The answer to laplacetransform 3t^2-9t is 6/(s^3)-9/(s^2)