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

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

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laplacetransform 3+7t+t^2

laplace transform

3 + 7 t + t^{2}

\frac{3}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}}

Solution steps

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

L {3} : \frac{3}{s}

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

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

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

Refine

\frac{3}{s} + 7 \frac{1}{s ^{2}} + \frac{2}{s ^{3}} : \frac{3}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}}

= \frac{3}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}}

x \to - 8 + lim (\frac{- 9 x}{x + 8})

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

\int \frac{1}{x ^{2} - 8 x + 15} d x

(x y + 4 y^{2} + 2 x^{2}) d x - (x^{2}) d y = 0

y = e^{9}

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