What is laplacetransform 3t^4+7t^2-5 ?

The answer to laplacetransform 3t^4+7t^2-5 is (72)/(s^5)+(14)/(s^3)-5/s

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laplacetransform 3t^4+7t^2-5

laplace transform

3 t^{4} + 7 t^{2} - 5

\frac{72}{s ^{5}} + \frac{14}{s ^{3}} - \frac{5}{s}

Solution steps

L {3 t^{4} + 7 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)}

= 3 L {t^{4}} + 7 L {t^{2}} - L {5}

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

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

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

= 3 \cdot \frac{24}{s ^{5}} + 7 \cdot \frac{2}{s ^{3}} - \frac{5}{s}

Refine

3 \frac{24}{s ^{5}} + 7 \frac{2}{s ^{3}} - \frac{5}{s} : \frac{72}{s ^{5}} + \frac{14}{s ^{3}} - \frac{5}{s}

= \frac{72}{s ^{5}} + \frac{14}{s ^{3}} - \frac{5}{s}

\int 6 + 3 cos (x) d x

\int \frac{5}{x ( x ^{4} + 7 )} d x

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

\int \frac{x - 2}{x + 1} d x

h \to 0 lim (\frac{f ( h ) ( 8 + h ) - f ( 8 )}{h})

What is laplacetransform 3t^4+7t^2-5 ?
The answer to laplacetransform 3t^4+7t^2-5 is (72)/(s^5)+(14)/(s^3)-5/s