What is laplacetransform 7+3t+2t^2-5t^3 ?

The answer to laplacetransform 7+3t+2t^2-5t^3 is 7/s+3/(s^2)+4/(s^3)-(30)/(s^4)

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laplacetransform 7+3t+2t^2-5t^3

laplace transform

7 + 3 t + 2 t^{2} - 5 t^{3}

\frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

Solution steps

L {7 + 3 t + 2 t^{2} - 5 t^{3}}

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 {7} + 3 L {t} + 2 L {t^{2}} - 5 L {t^{3}}

L {7} : \frac{7}{s}

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

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

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

= \frac{7}{s} + 3 \cdot \frac{1}{s ^{2}} + 2 \cdot \frac{2}{s ^{3}} - 5 \cdot \frac{6}{s ^{4}}

Refine

\frac{7}{s} + 3 \frac{1}{s ^{2}} + 2 \frac{2}{s ^{3}} - 5 \frac{6}{s ^{4}} : \frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

= \frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

What is laplacetransform 7+3t+2t^2-5t^3 ?
The answer to laplacetransform 7+3t+2t^2-5t^3 is 7/s+3/(s^2)+4/(s^3)-(30)/(s^4)