What is laplacetransform f(t)=7t+3 ?

The answer to laplacetransform f(t)=7t+3 is 7/(s^2)+3/s

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laplacetransform f(t)=7t+3

laplace transform

f (t) = 7 t + 3

\frac{7}{s ^{2}} + \frac{3}{s}

Solution steps

L {7 t + 3}

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)}

= 7 L {t} + L {3}

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

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

= 7 \cdot \frac{1}{s ^{2}} + \frac{3}{s}

Refine

7 \frac{1}{s ^{2}} + \frac{3}{s} : \frac{7}{s ^{2}} + \frac{3}{s}

= \frac{7}{s ^{2}} + \frac{3}{s}

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

\int_{1}^{4} \frac{1}{x - 1} d x

\int ln (1 - x) d x

\frac{d y}{d t} = 2 (t + 1) y, y (0) = 1

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

What is laplacetransform f(t)=7t+3 ?
The answer to laplacetransform f(t)=7t+3 is 7/(s^2)+3/s