What is laplacetransform cos(2t-2)e^{3t} ?

The answer to laplacetransform cos(2t-2)e^{3t} is (cos(2)(s-3)+2sin(2))/((s-3)^2+4)

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laplacetransform cos(2t-2)e^{3t}

laplace transform

cos (2 t - 2) e^{3 t}

\frac{cos ( 2 ) ( s - 3 ) + 2 sin ( 2 )}{( s - 3 ) ^{2} + 4}

Solution steps

L {e^{3 t} cos (2 t - 2)}

Apply transform rule:

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

then

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

For

cos (2 t - 2) e^{3 t} : f (t) = cos (2 t - 2), a = 3

= L {cos (2 t - 2)} (s - 3)

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

= \frac{cos ( 2 ) ( s - 3 ) + 2 sin ( 2 )}{( s - 3 ) ^{2} + 4}

\int_{0}^{1.75} 1500 x d x

\int \frac{1}{x ^{3} - 4 x ^{2} + 8 x} d x

x \to 3 lim (\frac{1}{6 - 2 x})

y^{^{''}} + 5 y^{^{'}} - 24 y = 0

\int \frac{3 x - 1}{x ^{2} - 3 x - 4} d x

What is laplacetransform cos(2t-2)e^{3t} ?
The answer to laplacetransform cos(2t-2)e^{3t} is (cos(2)(s-3)+2sin(2))/((s-3)^2+4)