What is laplacetransform 4t^3-24t+24sin(t) ?

The answer to laplacetransform 4t^3-24t+24sin(t) is (24)/(s^4(s^2+1))

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laplacetransform 4t^3-24t+24sin(t)

laplace transform

4 t^{3} - 24 t + 24 sin (t)

\frac{24}{s ^{4} ( s ^{2} + 1 )}

Solution steps

L {4 t^{3} - 24 t + 24 sin (t)}

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)}

= 4 L {t^{3}} - 24 L {t} + 24 L {sin (t)}

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

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

L {sin (t)} : \frac{1}{s ^{2} + 1}

= 4 \cdot \frac{6}{s ^{4}} - 24 \cdot \frac{1}{s ^{2}} + 24 \cdot \frac{1}{s ^{2} + 1}

Simplify

4 \frac{6}{s ^{4}} - 24 \frac{1}{s ^{2}} + 24 \frac{1}{s ^{2} + 1} : \frac{24}{s ^{4} ( s ^{2} + 1 )}

= \frac{24}{s ^{4} ( s ^{2} + 1 )}

What is laplacetransform 4t^3-24t+24sin(t) ?
The answer to laplacetransform 4t^3-24t+24sin(t) is (24)/(s^4(s^2+1))