What is laplacetransform (t+7)^3 ?

The answer to laplacetransform (t+7)^3 is 6/(s^4)+(42}{s^3}+(147)/(s^2)+\frac{343)/s

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laplacetransform (t+7)^3

laplace transform

(t + 7)^{3}

\frac{6}{s ^{4}} + \frac{42}{s ^{3}} + \frac{147}{s ^{2}} + \frac{343}{s}

Solution steps

L {(t + 7)^{3}}

Expand

(t + 7)^{3} : t^{3} + 21 t^{2} + 147 t + 343

= L {t^{3} + 21 t^{2} + 147 t + 343}

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^{3}} + 21 L {t^{2}} + 147 L {t} + L {343}

L {t^{3}} : \frac{6}{s ^{4}}

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

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

L {343} : \frac{343}{s}

= \frac{6}{s ^{4}} + 21 \cdot \frac{2}{s ^{3}} + 147 \cdot \frac{1}{s ^{2}} + \frac{343}{s}

Refine

\frac{6}{s ^{4}} + 21 \frac{2}{s ^{3}} + 147 \frac{1}{s ^{2}} + \frac{343}{s} : \frac{6}{s ^{4}} + \frac{42}{s ^{3}} + \frac{147}{s ^{2}} + \frac{343}{s}

= \frac{6}{s ^{4}} + \frac{42}{s ^{3}} + \frac{147}{s ^{2}} + \frac{343}{s}

\frac{t - t}{t ^{\frac{1}{6}}}

(2 x - 1)^{2}

\frac{d}{d x} (ln (x^{\frac{9}{2}}))

\int \frac{16}{( x ^{2} - 4 ) ( x - 2 )} d x

\frac{( ( \frac{d y}{d x} ) - e ^{- x} + 5 )}{y} = - 5

What is laplacetransform (t+7)^3 ?
The answer to laplacetransform (t+7)^3 is 6/(s^4)+(42}{s^3}+(147)/(s^2)+\frac{343)/s