What is laplacetransform 3t^2+15t+15 ?

The answer to laplacetransform 3t^2+15t+15 is 6/(s^3)+(15}{s^2}+\frac{15)/s

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laplacetransform 3t^2+15t+15

laplace transform

3 t^{2} + 15 t + 15

\frac{6}{s ^{3}} + \frac{15}{s ^{2}} + \frac{15}{s}

Solution steps

L {3 t^{2} + 15 t + 15}

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^{2}} + 15 L {t} + L {15}

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

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

L {15} : \frac{15}{s}

= 3 \cdot \frac{2}{s ^{3}} + 15 \cdot \frac{1}{s ^{2}} + \frac{15}{s}

Refine

3 \frac{2}{s ^{3}} + 15 \frac{1}{s ^{2}} + \frac{15}{s} : \frac{6}{s ^{3}} + \frac{15}{s ^{2}} + \frac{15}{s}

= \frac{6}{s ^{3}} + \frac{15}{s ^{2}} + \frac{15}{s}

y = (5 x^{2} - 1)^{- 3}

\int_{- \infty}^{0} x e^{8 x} d x

2 x^{2} - 4 x

\frac{\partial}{\partial z} (- z)

\int \frac{1}{( x - 2 ) ( x - 3 )} d x

What is laplacetransform 3t^2+15t+15 ?
The answer to laplacetransform 3t^2+15t+15 is 6/(s^3)+(15}{s^2}+\frac{15)/s