What is laplacetransform 4e^{-7t}cos(9t) ?

The answer to laplacetransform 4e^{-7t}cos(9t) is (4(s+7))/((s+7)^2+81)

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laplacetransform 4e^{-7t}cos(9t)

laplace transform

4 e^{- 7 t} cos (9 t)

\frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

Solution steps

L {4 e^{- 7 t} cos (9 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)}

= 4 L {e^{- 7 t} cos (9 t)}

L {e^{- 7 t} cos (9 t)} : \frac{s + 7}{( s + 7 ) ^{2} + 81}

= 4 \cdot \frac{s + 7}{( s + 7 ) ^{2} + 81}

Refine

4 \frac{s + 7}{( s + 7 ) ^{2} + 81} : \frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

= \frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

\int_{- \infty}^{0} \frac{1}{2 - 9 x} d x

\frac{d}{d x} (3 x^{2} + 9 x + 2)

\frac{d y}{d x} = 0

\int \frac{e ^{x + 3}}{x + 3} d x

What is laplacetransform 4e^{-7t}cos(9t) ?
The answer to laplacetransform 4e^{-7t}cos(9t) is (4(s+7))/((s+7)^2+81)