What is laplacetransform 8sin(3t)+2cos(2t) ?

The answer to laplacetransform 8sin(3t)+2cos(2t) is (24)/(s^2+9)+(2s)/(s^2+4)

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laplacetransform 8sin(3t)+2cos(2t)

laplace transform

8 sin (3 t) + 2 cos (2 t)

\frac{24}{s ^{2} + 9} + \frac{2 s}{s ^{2} + 4}

Solution steps

L {8 sin (3 t) + 2 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)}

= 8 L {sin (3 t)} + 2 L {cos (2 t)}

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

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

= 8 \cdot \frac{3}{s ^{2} + 9} + 2 \cdot \frac{s}{s ^{2} + 4}

Refine

8 \frac{3}{s ^{2} + 9} + 2 \frac{s}{s ^{2} + 4} : \frac{24}{s ^{2} + 9} + \frac{2 s}{s ^{2} + 4}

= \frac{24}{s ^{2} + 9} + \frac{2 s}{s ^{2} + 4}

\int \frac{e ^{s i n (x)}}{sec ( x )} d x

f (x) = (3 x^{3} + 5) (x^{4} - 5 x)

\int \frac{x + 5}{x ^{3} + 2 x ^{2} - x - 2} d x

2 y^{^{'}} = y

\frac{\partial}{\partial x} (4 sin^{2} (x))

What is laplacetransform 8sin(3t)+2cos(2t) ?
The answer to laplacetransform 8sin(3t)+2cos(2t) is (24)/(s^2+9)+(2s)/(s^2+4)