What is laplacetransform sin(2x)cos(2x) ?

The answer to laplacetransform sin(2x)cos(2x) is 2/(s^2+16)

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laplacetransform sin(2x)cos(2x)

laplace transform

sin (2 x) cos (2 x)

\frac{2}{s ^{2} + 16}

Solution steps

L {sin (2 x) cos (2 x)}

Rewrite using trig identities

L {\frac{1}{2} sin (4 x)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {sin (4 x)}

L {sin (4 x)} : \frac{4}{s ^{2} + 16}

= \frac{1}{2} \cdot \frac{4}{s ^{2} + 16}

Refine

\frac{1}{2} \frac{4}{s ^{2} + 16} : \frac{2}{s ^{2} + 16}

= \frac{2}{s ^{2} + 16}

\frac{d}{d x} (50 e^{4 x} + 300 e^{- 3 x})

\frac{\partial}{\partial x} (x^{2} e^{y})

e^{4 t s i n (2 t)}

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

\int (3 x^{2} + cos (x)) d x

What is laplacetransform sin(2x)cos(2x) ?
The answer to laplacetransform sin(2x)cos(2x) is 2/(s^2+16)