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

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

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

laplace transform

e^{3 t} cos (2 t)

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

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

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

\int 3 x cos^{3} (x^{2} + 2) d x

f (x) = x^{2}, at m (x) = - \frac{1}{2}

\frac{d}{d x} (r^{2} - 8 x^{2})

\int x (x + 4)^{- \frac{3}{2}} d x

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