What is inverse oflaplace ((s+2))/((s-1)(s+6)) ?

The answer to inverse oflaplace ((s+2))/((s-1)(s+6)) is 3/7 e^t+4/7 e^{-6t}

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inverse oflaplace ((s+2))/((s-1)(s+6))

inverse laplace

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

\frac{3}{7} e^{t} + \frac{4}{7} e^{- 6 t}

Solution steps

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

Take the partial fraction of

\frac{s + 2}{( s - 1 ) ( s + 6 )} : \frac{3}{7 ( s - 1 )} + \frac{4}{7 ( s + 6 )}

= L^{- 1} {\frac{3}{7 ( s - 1 )} + \frac{4}{7 ( 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{3}{7 ( s - 1 )}} + L^{- 1} {\frac{4}{7 ( s + 6 )}}

L^{- 1} {\frac{3}{7 ( s - 1 )}} : \frac{3}{7} e^{t}

L^{- 1} {\frac{4}{7 ( s + 6 )}} : \frac{4}{7} e^{- 6 t}

= \frac{3}{7} e^{t} + \frac{4}{7} e^{- 6 t}

x \to \frac{π}{2} lim (cos (x))

\int \frac{1}{x x ^{2} - 64} d x

\int \frac{x ^{2}}{12} d x

f (x) = 8 6 x^{2} + 7

What is inverse oflaplace ((s+2))/((s-1)(s+6)) ?
The answer to inverse oflaplace ((s+2))/((s-1)(s+6)) is 3/7 e^t+4/7 e^{-6t}