What is laplacetransform t^3+4t^2+5 ?

The answer to laplacetransform t^3+4t^2+5 is 6/(s^4)+8/(s^3)+5/s

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laplacetransform t^3+4t^2+5

laplace transform

t^{3} + 4 t^{2} + 5

\frac{6}{s ^{4}} + \frac{8}{s ^{3}} + \frac{5}{s}

Solution steps

L {t^{3} + 4 t^{2} + 5}

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}} + 4 L {t^{2}} + L {5}

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

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

L {5} : \frac{5}{s}

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

Refine

\frac{6}{s ^{4}} + 4 \frac{2}{s ^{3}} + \frac{5}{s} : \frac{6}{s ^{4}} + \frac{8}{s ^{3}} + \frac{5}{s}

= \frac{6}{s ^{4}} + \frac{8}{s ^{3}} + \frac{5}{s}

\frac{d}{d x} (6 e^{x} + 2)

\int_{0}^{\frac{π}{2}} sin^{7} (y) d y

\int 1 - (- 2 sin^{2} (x + 4))^{2} d x

\frac{3}{s}

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} + 6 x}{x ^{2} - 9})

What is laplacetransform t^3+4t^2+5 ?
The answer to laplacetransform t^3+4t^2+5 is 6/(s^4)+8/(s^3)+5/s