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

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

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

laplace transform

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

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

Solution steps

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

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

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

L {e^{- 2 t} cos (3 t)} : \frac{s + 2}{( s + 2 ) ^{2} + 9}

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

Refine

2 \frac{s + 2}{( s + 2 ) ^{2} + 9} : \frac{2 ( s + 2 )}{( s + 2 ) ^{2} + 9}

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

\int \frac{1}{2} e^{x} sin (x) d x

\frac{1}{2002 s ^{2} + 4}

\int \frac{2 x}{4 + x ^{2}} d x

\frac{d}{d x} (e^{c o s (x) + l n (x)})

3 arcsin (x)

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