What is laplacetransform sin^2(6t) ?

The answer to laplacetransform sin^2(6t) is (72)/(s(s^2+144))

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laplacetransform sin^2(6t)

laplace transform

sin^{2} (6 t)

\frac{72}{s ( s ^{2} + 144 )}

Solution steps

L {sin^{2} (6 t)}

Rewrite using trig identities

L {\frac{1}{2} - \frac{1}{2} cos (12 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 {\frac{1}{2}} - \frac{1}{2} L {cos (12 t)}

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

L {cos (12 t)} : \frac{s}{s ^{2} + 144}

= \frac{1}{2 s} - \frac{1}{2} \cdot \frac{s}{s ^{2} + 144}

Simplify

\frac{1}{2 s} - \frac{1}{2} \frac{s}{s ^{2} + 144} : \frac{72}{s ( s ^{2} + 144 )}

= \frac{72}{s ( s ^{2} + 144 )}

\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

\frac{d}{d x} (x^{3} + x^{5})

\frac{d}{d x} (- 5 cot (x) + 3 sec (x))

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

x \to \infty lim (7 x - 3)

What is laplacetransform sin^2(6t) ?
The answer to laplacetransform sin^2(6t) is (72)/(s(s^2+144))