What is inverse oflaplace ((s+7))/(s^2+11s+30) ?

The answer to inverse oflaplace ((s+7))/(s^2+11s+30) is 2e^{-5t}-e^{-6t}

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inverse oflaplace ((s+7))/(s^2+11s+30)

inverse laplace

\frac{( s + 7 )}{s ^{2} + 11 s + 30}

2 e^{- 5 t} - e^{- 6 t}

Solution steps

L^{- 1} {\frac{( s + 7 )}{s ^{2} + 11 s + 30}}

Take the partial fraction of

\frac{s + 7}{s ^{2} + 11 s + 30} : \frac{2}{s + 5} - \frac{1}{s + 6}

= L^{- 1} {\frac{2}{s + 5} - \frac{1}{s + 6}}

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 + 5}} - L^{- 1} {\frac{1}{s + 6}}

L^{- 1} {\frac{2}{s + 5}} : 2 e^{- 5 t}

L^{- 1} {\frac{1}{s + 6}} : e^{- 6 t}

= 2 e^{- 5 t} - e^{- 6 t}

\frac{d}{d x} (\frac{x ^{n}}{n ^{2}})

\int_{- \infty}^{0} \frac{1}{3 - 2 x} d x

e^{- m x}

\frac{d ^{2}}{d x ^{2}} (11 tan (\frac{x}{10}))

f (x) = 4 sin^{2} (0.5 x) + 1

What is inverse oflaplace ((s+7))/(s^2+11s+30) ?
The answer to inverse oflaplace ((s+7))/(s^2+11s+30) is 2e^{-5t}-e^{-6t}