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

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

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inverse oflaplace 4/(s+5)

inverse laplace

\frac{4}{s + 5}

4 e^{- 5 t}

Solution steps

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

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

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

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

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

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

= 4 e^{- 5 t}

\frac{d}{d x} (- 4 e^{x} sin (x))

\int \frac{1}{x ^{4} 16 - 25 x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} - 16}{x + 4})

(x^{2} + 3) (x^{2} - 3) x^{2}

\int sec^{2} (x) tan^{2} (x) d x

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