What is laplacetransform s^2+6 ?

The answer to laplacetransform s^2+6 is 2/(s^3)+6/s

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laplacetransform s^2+6

laplace transform

s^{2} + 6

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

Solution steps

L {s^{2} + 6}

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 {s^{2}} + L {6}

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

L {6} : \frac{6}{s}

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

f (x) = 8 x^{3} - 2 x^{2} + 2 x, at x = 2

\int_{0}^{t} sin (2 s) d s

\int \frac{2}{10 + 6 x + x ^{2}} d x

\frac{1}{4 x}

\int (1 - x) (1 - 2 x) (1 - 3 x) d x

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