What is laplacetransform cos^2(5t) ?

The answer to laplacetransform cos^2(5t) is 1/(2s)+s/(2(s^2+100))

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laplacetransform cos^2(5t)

laplace transform

cos^{2} (5 t)

\frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 100 )}

Solution steps

L {cos^{2} (5 t)}

Rewrite using trig identities

L {\frac{1}{2} + \frac{1}{2} cos (10 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 (10 t)}

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

L {cos (10 t)} : \frac{s}{s ^{2} + 100}

= \frac{1}{2 s} + \frac{1}{2} \cdot \frac{s}{s ^{2} + 100}

Refine

\frac{1}{2 s} + \frac{1}{2} \frac{s}{s ^{2} + 100} : \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 100 )}

= \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 100 )}

\int_{0}^{\infty} \frac{3}{x ^{2} + 4} d x

x y y^{^{'}} = 2 (2 x^{2} + y^{2})

\frac{d}{d x} (\frac{tan ( 2 x ) - 1}{x ^{2}})

0.0018425 (t + 7)^{4.5}

y = x^{2} ln (2 x)

What is laplacetransform cos^2(5t) ?
The answer to laplacetransform cos^2(5t) is 1/(2s)+s/(2(s^2+100))