What is laplacetransform (t+1)^2 ?

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

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laplacetransform (t+1)^2

laplace transform

(t + 1)^{2}

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

Solution steps

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

Expand

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

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

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

L {t} : \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{4 x + 6}{( x ^{2} + 2 ) \cdot ( x + 2 )} d x

f (x) = x^{\frac{5}{3}} - x^{\frac{2}{3}}

e^{- t} t

\frac{1}{x - 3}

\int \frac{2 e ^{2 r}}{7 + e ^{2 r}} d r

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