What is laplacetransform s^2+2s+1 ?

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

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laplacetransform s^2+2s+1

laplace transform

s^{2} + 2 s + 1

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

Solution steps

L {s^{2} + 2 s + 1}

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 {s^{2}} + 2 L {s} + L {1}

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

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

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

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

Refine

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

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

y = x^{2} e^{x} - 2 x e^{x} + 4 e^{x}

\int (x - π) sin (x) d x

\int_{0}^{5} 1 d x

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 1

1 + 2 x^{2}

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