What is inverse oflaplace ((s+5))/(s^2+5s+6) ?

The answer to inverse oflaplace ((s+5))/(s^2+5s+6) is 3e^{-2t}-2e^{-3t}

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inverse oflaplace ((s+5))/(s^2+5s+6)

inverse laplace

\frac{( s + 5 )}{s ^{2} + 5 s + 6}

3 e^{- 2 t} - 2 e^{- 3 t}

Solution steps

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

Take the partial fraction of

\frac{s + 5}{s ^{2} + 5 s + 6} : \frac{3}{s + 2} - \frac{2}{s + 3}

= L^{- 1} {\frac{3}{s + 2} - \frac{2}{s + 3}}

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{3}{s + 2}} - L^{- 1} {\frac{2}{s + 3}}

L^{- 1} {\frac{3}{s + 2}} : 3 e^{- 2 t}

L^{- 1} {\frac{2}{s + 3}} : 2 e^{- 3 t}

= 3 e^{- 2 t} - 2 e^{- 3 t}

\int x^{6} + e^{2 x} d x

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\int sec^{3} (x) cos (x) d x

\frac{\partial}{\partial y} (ln (x - y))

\frac{d}{d x} (x (e^{x} - 1))

What is inverse oflaplace ((s+5))/(s^2+5s+6) ?
The answer to inverse oflaplace ((s+5))/(s^2+5s+6) is 3e^{-2t}-2e^{-3t}