What is laplacetransform t^{3/2}*e^{-2t} ?

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

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laplacetransform t^{3/2}*e^{-2t}

laplace transform

t^{\frac{3}{2}} \cdot e^{- 2 t}

\frac{3 π}{4 ( s + 2 ) ^{\frac{5}{2}}}

Solution steps

L {e^{- 2 t} t^{\frac{3}{2}}}

Apply transform rule:

L {f (t)} = F (s)

then

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

For

t^{\frac{3}{2}} e^{- 2 t} : f (t) = t^{\frac{3}{2}}, a = - 2

= L {t^{\frac{3}{2}}} (s + 2)

L {t^{\frac{3}{2}}} : \frac{3 π}{4 s ^{\frac{5}{2}}}

= \frac{3 π}{4 ( s + 2 ) ^{\frac{5}{2}}}

\frac{\partial}{\partial s} (\frac{t}{s})

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 1} d x

\int \frac{1}{5} x d x

\int \frac{2}{x ^{3} x ^{4} - 81} d x

\frac{d}{d t} (e^{- a t} cos (wt))

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