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

The answer to laplacetransform e^{-t}sin(3t) is 3/((s+1)^2+9)

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laplacetransform e^{-t}sin(3t)

laplace transform

e^{- t} sin (3 t)

\frac{3}{( s + 1 ) ^{2} + 9}

Solution steps

L {e^{- t} sin (3 t)}

Apply transform rule:

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

then

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

For

e^{- t} sin (3 t) : f (t) = sin (3 t), a = - 1

= L {sin (3 t)} (s + 1)

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= \frac{3}{( s + 1 ) ^{2} + 9}

What is laplacetransform e^{-t}sin(3t) ?
The answer to laplacetransform e^{-t}sin(3t) is 3/((s+1)^2+9)