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

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

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laplacetransform 3t^2+3t-2

laplace transform

3 t^{2} + 3 t - 2

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

Solution steps

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

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

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

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

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

Refine

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

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

\int \frac{ln ( 3 x )}{x ^{3}} d x

\int 2 x - 3 e^{x} d x

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

\int \frac{y ^{2}}{y + 1} d y

\frac{d}{d x} (2 sec (x))

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