What is laplacetransform 8e^{-6t}cos(4t+30) ?

The answer to laplacetransform 8e^{-6t}cos(4t+30) is (8(cos(30)(s+6)-4sin(30)))/((s+6)^2+16)

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laplacetransform 8e^{-6t}cos(4t+30)

laplace transform

8 e^{- 6 t} cos (4 t + 30)

\frac{8 ( cos ( 30 ) ( s + 6 ) - 4 sin ( 30 ) )}{( s + 6 ) ^{2} + 16}

Solution steps

L {8 e^{- 6 t} cos (4 t + 30)}

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)}

= 8 L {e^{- 6 t} cos (4 t + 30)}

L {e^{- 6 t} cos (4 t + 30)} : \frac{cos ( 30 ) ( s + 6 ) - 4 sin ( 30 )}{( s + 6 ) ^{2} + 16}

= 8 \cdot \frac{cos ( 30 ) ( s + 6 ) - 4 sin ( 30 )}{( s + 6 ) ^{2} + 16}

Refine

8 \frac{cos ( 30 ) ( s + 6 ) - 4 sin ( 30 )}{( s + 6 ) ^{2} + 16} : \frac{8 ( cos ( 30 ) ( s + 6 ) - 4 sin ( 30 ) )}{( s + 6 ) ^{2} + 16}

= \frac{8 ( cos ( 30 ) ( s + 6 ) - 4 sin ( 30 ) )}{( s + 6 ) ^{2} + 16}

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\int x sin (3 x - 2) d x

- cos (2 t)

\int 21 x sec^{2} (x) d x

What is laplacetransform 8e^{-6t}cos(4t+30) ?
The answer to laplacetransform 8e^{-6t}cos(4t+30) is (8(cos(30)(s+6)-4sin(30)))/((s+6)^2+16)