What is laplacetransform (t+5)^3 ?

The answer to laplacetransform (t+5)^3 is 6/(s^4)+(30}{s^3}+(75)/(s^2)+\frac{125)/s

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laplacetransform (t+5)^3

laplace transform

(t + 5)^{3}

\frac{6}{s ^{4}} + \frac{30}{s ^{3}} + \frac{75}{s ^{2}} + \frac{125}{s}

Solution steps

L {(t + 5)^{3}}

Expand

(t + 5)^{3} : t^{3} + 15 t^{2} + 75 t + 125

= L {t^{3} + 15 t^{2} + 75 t + 125}

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}} + 15 L {t^{2}} + 75 L {t} + L {125}

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

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

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

L {125} : \frac{125}{s}

= \frac{6}{s ^{4}} + 15 \cdot \frac{2}{s ^{3}} + 75 \cdot \frac{1}{s ^{2}} + \frac{125}{s}

Refine

\frac{6}{s ^{4}} + 15 \frac{2}{s ^{3}} + 75 \frac{1}{s ^{2}} + \frac{125}{s} : \frac{6}{s ^{4}} + \frac{30}{s ^{3}} + \frac{75}{s ^{2}} + \frac{125}{s}

= \frac{6}{s ^{4}} + \frac{30}{s ^{3}} + \frac{75}{s ^{2}} + \frac{125}{s}

\frac{d}{d x} (\frac{ln ( x )}{x ^{13}})

\frac{10}{x}

x \to a lim (\frac{x - 1}{3 x + 6})

\int (x ln (x)) d x

\frac{d}{d x} (π r (x) (x)^{2} h)

What is laplacetransform (t+5)^3 ?
The answer to laplacetransform (t+5)^3 is 6/(s^4)+(30}{s^3}+(75)/(s^2)+\frac{125)/s