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

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

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

laplace transform

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

\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

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

f (x) = - 8 x^{2} - 7 x, at x = - 4

\int \frac{x ^{2} - 3 x + 12}{( x ^{2} - 4 x + 11 ) ^{2}} d x

\frac{d}{d x} (\frac{1}{x ^{3}} - \frac{2}{x ^{2}})

(x^{4} + 7 x^{2} - 3)^{4}

f (x) = \frac{5}{x ^{2}}, at x = 1

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