What is laplacetransform 1+3t+3t^2 ?

The answer to laplacetransform 1+3t+3t^2 is 1/s+3/(s^2)+6/(s^3)

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laplacetransform 1+3t+3t^2

laplace transform

1 + 3 t + 3 t^{2}

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

Solution steps

L {1 + 3 t + 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)}

= L {1} + 3 L {t} + 3 L {t^{2}}

L {1} : \frac{1}{s}

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

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

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

Refine

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

= \frac{1}{s} + \frac{3}{s ^{2}} + \frac{6}{s ^{3}}

\frac{d}{d x} (\frac{sin ( x + 1 )}{e ^{x}})

\frac{e ^{- 4 x}}{( x - 2 ) ^{2}}

x \to \infty lim ((1 + \frac{c}{x})^{2 x})

\int (10 x^{9} - \frac{9}{x ^{9}}) d x

x \to 1 lim (x^{4} e^{- x^{2}})

What is laplacetransform 1+3t+3t^2 ?
The answer to laplacetransform 1+3t+3t^2 is 1/s+3/(s^2)+6/(s^3)