What is laplacetransform cos^2(x) ?

The answer to laplacetransform cos^2(x) is 1/(2s)+s/(2(s^2+4))

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laplacetransform cos^2(x)

laplace transform

cos^{2} (x)

\frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 4 )}

Solution steps

L {cos^{2} (x)}

Use the following identity:

cos^{2} (x) = \frac{1}{2} + cos (2 x) \frac{1}{2}

= L {\frac{1}{2} + cos (2 x) \frac{1}{2}}

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 (2 x)}

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

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

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

Refine

\frac{1}{2 s} + \frac{1}{2} \frac{s}{s ^{2} + 4} : \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 4 )}

= \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 4 )}

\frac{d}{d x} (e^{4 y - x^{2} - y^{2}})

\int_{\frac{π}{4}}^{\infty} \frac{7}{x} d x

n = 1 \sum \infty \frac{n ^{2}}{3 ^{n}}

\frac{d}{d x} (x^{n})

\int_{0}^{2} x^{5} \cdot e^{x^{2}} d x

What is laplacetransform cos^2(x) ?
The answer to laplacetransform cos^2(x) is 1/(2s)+s/(2(s^2+4))