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

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

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inverse oflaplace 1/(sqrt(2s+3))

inverse laplace

\frac{1}{2 s + 3}

\frac{e ^{- \frac{3 t}{2}}}{2 π t}

Solution steps

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

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {F (s - a)} = e^{a t} f (t)

For

\frac{1}{2 s + 3} : a = - \frac{3}{2}, F (s) = \frac{1}{2 s}

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

L^{- 1} {\frac{1}{2 s}} : \frac{1}{2 π t}

= \frac{e ^{- \frac{3 t}{2}}}{2 π t}

\frac{\partial}{\partial x} (x \cdot e^{x + 2 y})

x \to \infty lim (\frac{sin ( 13 x )}{3 x})

\frac{d}{d x} ((x + 2 y) (x^{2} y + x y^{2}))

f (x) = x^{3} - 27 x + 9

\int \frac{5}{( 5 x + 2 ) ln ( 5 x + 2 )} d x

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