What is inverse oflaplace 1/(3s-2) ?

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

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inverse oflaplace 1/(3s-2)

inverse laplace

\frac{1}{3 s - 2}

\frac{1}{3} e^{\frac{2 t}{3}}

Solution steps

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

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

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

Use Inverse Laplace Transform table:

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

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

= \frac{1}{3} e^{\frac{2 t}{3}}

\frac{e ^{x}}{1 - x}

\int (x^{2} + 1) e^{- 2 x} d x

\int (\frac{sec ( x ) tan ( x )}{sec ( x ) - 7}) d x

\int \frac{2}{3 x ^{2}} d x

\frac{d}{d x} (arctan (2 x^{2}))

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