What is laplacetransform 3-2t+4cos(2t) ?

The answer to laplacetransform 3-2t+4cos(2t) is 3/s-2/(s^2)+(4s)/(s^2+4)

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laplacetransform 3-2t+4cos(2t)

laplace transform

3 - 2 t + 4 cos (2 t)

\frac{3}{s} - \frac{2}{s ^{2}} + \frac{4 s}{s ^{2} + 4}

Solution steps

L {3 - 2 t + 4 cos (2 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)}

= L {3} - 2 L {t} + 4 L {cos (2 t)}

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

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

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

= \frac{3}{s} - 2 \cdot \frac{1}{s ^{2}} + 4 \cdot \frac{s}{s ^{2} + 4}

Refine

\frac{3}{s} - 2 \frac{1}{s ^{2}} + 4 \frac{s}{s ^{2} + 4} : \frac{3}{s} - \frac{2}{s ^{2}} + \frac{4 s}{s ^{2} + 4}

= \frac{3}{s} - \frac{2}{s ^{2}} + \frac{4 s}{s ^{2} + 4}

\frac{d}{d x} (x cos^{2} (x))

x \to 1 + lim (\frac{5}{x ^{2} - 1})

\int \frac{1}{1 + 2 x} d x

x \to 3 lim (4 x)

x \to 3 lim (5 x^{3} - 4 x^{2} + x - 6)

What is laplacetransform 3-2t+4cos(2t) ?
The answer to laplacetransform 3-2t+4cos(2t) is 3/s-2/(s^2)+(4s)/(s^2+4)