What is laplacetransform t^{(3/2)} ?

The answer to laplacetransform t^{(3/2)} is (3sqrt(pi))/(4s^{5/2)}

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laplacetransform t^{(3/2)}

laplace transform

t^{(\frac{3}{2})}

\frac{3 π}{4 s ^{\frac{5}{2}}}

Solution steps

L {t^{(\frac{3}{2})}}

Use Laplace Transform table:

L {t^{n - 1/2}} = \frac{( 2 n - 1 ) !! π}{2 ^{n} s ^{n + 1/2}}

L {t^{\frac{3}{2}}} = \frac{3 π}{2 ^{2} s ^{\frac{5}{2}}}

= \frac{3 π}{2 ^{2} s ^{\frac{5}{2}}}

= \frac{3 π}{4 s ^{\frac{5}{2}}}

\frac{x ^{2}}{x - 5}

x = 9 - y^{2}, x = y^{2} - 9

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

\int \frac{1}{x ^{\frac{3}{2}} + 3 x + 2 x ^{\frac{1}{2}}} d x

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

What is laplacetransform t^{(3/2)} ?
The answer to laplacetransform t^{(3/2)} is (3sqrt(pi))/(4s^{5/2)}