What is laplacetransform 3t^4-2t^2+1 ?

The answer to laplacetransform 3t^4-2t^2+1 is (72)/(s^5)-4/(s^3)+1/s

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laplacetransform 3t^4-2t^2+1

laplace transform

3 t^{4} - 2 t^{2} + 1

\frac{72}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

Solution steps

L {3 t^{4} - 2 t^{2} + 1}

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)}

= 3 L {t^{4}} - 2 L {t^{2}} + L {1}

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

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

L {1} : \frac{1}{s}

= 3 \cdot \frac{24}{s ^{5}} - 2 \cdot \frac{2}{s ^{3}} + \frac{1}{s}

Refine

3 \frac{24}{s ^{5}} - 2 \frac{2}{s ^{3}} + \frac{1}{s} : \frac{72}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

= \frac{72}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

cos (2 t)

y = 16 - x^{2}

\frac{\partial}{\partial x} ((a - x)^{2} + b (y - x^{2})^{2})

\int 6 x^{2} y d y

What is laplacetransform 3t^4-2t^2+1 ?
The answer to laplacetransform 3t^4-2t^2+1 is (72)/(s^5)-4/(s^3)+1/s