What is laplacetransform (t-5)/5 ?

The answer to laplacetransform (t-5)/5 is 1/(5s^2)-1/s

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laplacetransform (t-5)/5

laplace transform

\frac{t - 5}{5}

\frac{1}{5 s ^{2}} - \frac{1}{s}

Solution steps

L {\frac{t - 5}{5}}

Expand

= L {\frac{t}{5} - \frac{5}{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)}

= \frac{1}{5} L {t} - L {\frac{5}{5}}

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

L {\frac{5}{5}} : \frac{1}{s}

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

Refine

\frac{1}{5} \frac{1}{s ^{2}} - \frac{1}{s} : \frac{1}{5 s ^{2}} - \frac{1}{s}

= \frac{1}{5 s ^{2}} - \frac{1}{s}

\int sin^{3} (11 x) d x

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\frac{π}{2}

\int \frac{3 + 4 x}{7 + 3 x + 2 x ^{2}} d x

x \to - 2 lim (\frac{x + 2}{x ^{2} - 4})

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