Question

can any one find Laplace below?

Answer 1

\[e ^{x} \frac{ sinx }{ x}\]

Answer 2

\(f(t)=e^t\frac{\sin t}t\\F(s)=\mathcal{L}\{f(t)\}=\mathcal{L}\{e^t\frac{\sin t}t\}=[\mathcal{L}\{\frac{\sin t}t\}](s-1)=\arctan\left(\frac1{s-1}\right)\)

Answer 3

I used this: http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf

Answer 4

From Mathematica 8:\[\text{LaplaceTransform}\left[E{}^{\wedge}x \frac{\text{Sin}[x]}{x},x,s\right]\to \text{ArcTan}\left[\frac{1}{-1+s}\right] \]