What is inverse oflaplace 4/(s(5s+1)) ?

The answer to inverse oflaplace 4/(s(5s+1)) is 4\H(t)-4e^{-t/5}

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inverse oflaplace 4/(s(5s+1))

inverse laplace

\frac{4}{s ( 5 s + 1 )}

4 H (t) - 4 e^{- \frac{t}{5}}

Solution steps

L^{- 1} {\frac{4}{s ( 5 s + 1 )}}

Take the partial fraction of

\frac{4}{s ( 5 s + 1 )} : \frac{4}{s} - \frac{20}{5 s + 1}

= L^{- 1} {\frac{4}{s} - \frac{20}{5 s + 1}}

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{4}{s}} - L^{- 1} {\frac{20}{5 s + 1}}

L^{- 1} {\frac{4}{s}} : 4 H (t)

L^{- 1} {\frac{20}{5 s + 1}} : 4 e^{- \frac{t}{5}}

= 4 H (t) - 4 e^{- \frac{t}{5}}

What is inverse oflaplace 4/(s(5s+1)) ?
The answer to inverse oflaplace 4/(s(5s+1)) is 4\H(t)-4e^{-t/5}