What is laplacetransform 3sin^2(t) ?

The answer to laplacetransform 3sin^2(t) is 6/(s(s^2+4))

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laplacetransform 3sin^2(t)

laplace transform

3 sin^{2} (t)

\frac{6}{s ( s ^{2} + 4 )}

Solution steps

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

Rewrite using trig identities

L {\frac{3}{2} - \frac{3}{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)}

= L {\frac{3}{2}} - \frac{3}{2} L {cos (2 t)}

L {\frac{3}{2}} : \frac{3}{2 s}

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

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

Simplify

\frac{3}{2 s} - \frac{3}{2} \frac{s}{s ^{2} + 4} : \frac{6}{s ( s ^{2} + 4 )}

= \frac{6}{s ( s ^{2} + 4 )}

\frac{\partial}{\partial x} (y^{2} + 6 x - x^{2} y + 36)

\int 2 t d t

\int (4 x + 4) 2 x^{2} + 4 x d x

\int 50 x d x

x - 1, x - 1

What is laplacetransform 3sin^2(t) ?
The answer to laplacetransform 3sin^2(t) is 6/(s(s^2+4))