What is inverse oflaplace 2/(s+1)+32*s/(s^2+9) ?

The answer to inverse oflaplace 2/(s+1)+32*s/(s^2+9) is 2e^{-t}+32cos(3t)

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inverse oflaplace 2/(s+1)+32*s/(s^2+9)

inverse laplace

\frac{2}{s + 1} + 32 \cdot \frac{s}{s ^{2} + 9}

2 e^{- t} + 32 cos (3 t)

Solution steps

L^{- 1} {\frac{2}{s + 1} + 32 \cdot \frac{s}{s ^{2} + 9}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{2}{s + 1}} + 32 L^{- 1} {\frac{s}{s ^{2} + 9}}

L^{- 1} {\frac{2}{s + 1}} : 2 e^{- t}

L^{- 1} {\frac{s}{s ^{2} + 9}} : cos (3 t)

= 2 e^{- t} + 32 cos (3 t)

f (x) = x^{4}, (- 1, 1)

y = 4 x - 2 x^{2}

\frac{d}{d x} ((a x + b)^{n})

f (x) = \frac{x ^{2}}{2} + 2 x + 4

f^{^{'}} (x) = \frac{9}{2 9 x - 5}

What is inverse oflaplace 2/(s+1)+32*s/(s^2+9) ?
The answer to inverse oflaplace 2/(s+1)+32*s/(s^2+9) is 2e^{-t}+32cos(3t)