What is laplacetransform 14t-sin(7t) ?

The answer to laplacetransform 14t-sin(7t) is (14)/(s^2)-7/(s^2+49)

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laplacetransform 14t-sin(7t)

laplace transform

14 t - sin (7 t)

\frac{14}{s ^{2}} - \frac{7}{s ^{2} + 49}

Solution steps

L {14 t - sin (7 t)}

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)}

= 14 L {t} - L {sin (7 t)}

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

L {sin (7 t)} : \frac{7}{s ^{2} + 49}

= 14 \cdot \frac{1}{s ^{2}} - \frac{7}{s ^{2} + 49}

Refine

14 \frac{1}{s ^{2}} - \frac{7}{s ^{2} + 49} : \frac{14}{s ^{2}} - \frac{7}{s ^{2} + 49}

= \frac{14}{s ^{2}} - \frac{7}{s ^{2} + 49}

\int (e^{x} cos (x)) d x

x \to 2 lim (x (x - 1))

x, 2

\int cos (2 ln (x)) d x

What is laplacetransform 14t-sin(7t) ?
The answer to laplacetransform 14t-sin(7t) is (14)/(s^2)-7/(s^2+49)