What is laplacetransform F(x)=e^{2x}cos(2x) ?

The answer to laplacetransform F(x)=e^{2x}cos(2x) is (s-2)/((s-2)^2+4)

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laplacetransform F(x)=e^{2x}cos(2x)

laplace transform

F (x) = e^{2 x} cos (2 x)

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

Solution steps

L {e^{2 x} cos (2 x)}

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

e^{2 x} cos (2 x) : f (x) = cos (2 x), a = 2

= L {cos (2 x)} (s - 2)

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

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

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

What is laplacetransform F(x)=e^{2x}cos(2x) ?
The answer to laplacetransform F(x)=e^{2x}cos(2x) is (s-2)/((s-2)^2+4)