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

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

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inverse oflaplace 1/(4s+1)

inverse laplace

\frac{1}{4 s + 1}

\frac{1}{4} e^{- \frac{t}{4}}

Solution steps

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

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

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)}

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

Use Inverse Laplace Transform table:

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

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

= \frac{1}{4} e^{- \frac{t}{4}}

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

f (x) = \frac{2 x - 6}{x - 1}

\frac{d y}{d x} = y^{\frac{1}{2}}

\int \frac{72}{1 - cos ( 8 x )} d x

e^{- x^{4}}

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