What is laplacetransform (x+1)^2 ?

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

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laplacetransform (x+1)^2

laplace transform

(x + 1)^{2}

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

Solution steps

L {(x + 1)^{2}}

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= L {x^{2} + 2 x + 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 {x^{2}} + 2 L {x} + L {1}

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

L {x} : \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}

\int \frac{- x ^{2} cos ( x )}{4} d x

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}) - z)

y = x^{8 x}

\frac{\partial}{\partial x} (e^{s i n (x + y)})

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