What is laplacetransform (e^t)/(sqrt(t)) ?

The answer to laplacetransform (e^t)/(sqrt(t)) is sqrt(pi/(s-1))

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laplacetransform (e^t)/(sqrt(t))

laplace transform

\frac{e ^{t}}{t}

\frac{π}{s - 1}

Solution steps

L {\frac{e ^{t}}{t}}

Apply transform rule:

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

then

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

For

\frac{e ^{t}}{t} : f (t) = \frac{1}{t}, a = 1

= L {\frac{1}{t}} (s - 1)

L {\frac{1}{t}} : \frac{π}{s}

= \frac{π}{( s - 1 )}

= \frac{π}{s - 1}

\int x cos (\frac{mπ x}{2}) d x

\frac{d}{d x} ((\frac{3}{5})^{x})

\int sec (t) (4 sec (t) + 7 tan (t)) d t

\frac{d}{d y} (y e^{x})

x \to - \infty lim (x^{- 2})

What is laplacetransform (e^t)/(sqrt(t)) ?
The answer to laplacetransform (e^t)/(sqrt(t)) is sqrt(pi/(s-1))