What is laplacetransform 3sin(t)cos(t) ?

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

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laplacetransform 3sin(t)cos(t)

laplace transform

3 sin (t) cos (t)

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

Solution steps

L {3 sin (t) cos (t)}

Rewrite using trig identities

L {\frac{3}{2} sin (2 t)}

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

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

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

Refine

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

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

\frac{3}{s ^{3}}

y^{^{'}} + 10 x^{4} y = 50 x^{9} e^{3 x^{5}}

\int 4 sin^{3} (2 x) d x

\int 13 - x d x

x \to - 1 lim (\frac{4}{x ^{2} + 2 x + 3})

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