What is laplacetransform (2+t)^4 ?

The answer to laplacetransform (2+t)^4 is (16)/s+(32)/(s^2)+(48)/(s^3)+(48)/(s^4)+(24)/(s^5)

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laplacetransform (2+t)^4

laplace transform

(2 + t)^{4}

\frac{16}{s} + \frac{32}{s ^{2}} + \frac{48}{s ^{3}} + \frac{48}{s ^{4}} + \frac{24}{s ^{5}}

Solution steps

L {(2 + t)^{4}}

Expand

(2 + t)^{4} : 16 + 32 t + 24 t^{2} + 8 t^{3} + t^{4}

= L {16 + 32 t + 24 t^{2} + 8 t^{3} + t^{4}}

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 {16} + 32 L {t} + 24 L {t^{2}} + 8 L {t^{3}} + L {t^{4}}

L {16} : \frac{16}{s}

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

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

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

L {t^{4}} : \frac{24}{s ^{5}}

= \frac{16}{s} + 32 \cdot \frac{1}{s ^{2}} + 24 \cdot \frac{2}{s ^{3}} + 8 \cdot \frac{6}{s ^{4}} + \frac{24}{s ^{5}}

Refine

\frac{16}{s} + 32 \frac{1}{s ^{2}} + 24 \frac{2}{s ^{3}} + 8 \frac{6}{s ^{4}} + \frac{24}{s ^{5}} : \frac{16}{s} + \frac{32}{s ^{2}} + \frac{48}{s ^{3}} + \frac{48}{s ^{4}} + \frac{24}{s ^{5}}

= \frac{16}{s} + \frac{32}{s ^{2}} + \frac{48}{s ^{3}} + \frac{48}{s ^{4}} + \frac{24}{s ^{5}}

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What is laplacetransform (2+t)^4 ?
The answer to laplacetransform (2+t)^4 is (16)/s+(32)/(s^2)+(48)/(s^3)+(48)/(s^4)+(24)/(s^5)