# Laplace transformation of $\frac{\cos x}{x}$

How would you find the laplace transformation of $\frac{\cos x}{x}$?
Like I know you need to add it to another transformation to solve for it. And I know that the transformation of $\cos x$ is $\frac{s}{s^2+1}$ and the transformation of $\frac{f(x)} {x}$ is $\int_s^\infty \! F(u) \, \mathrm{d}u$.

And I know that for the transformation of $\frac{\sin x}{x}$ you apply it to the integral multiplying $e^{-sx}$ I am just having trouble trying to apply this with $\cos$. And actually how it works all together.
I am trying to further understand how this concept actually works. thanks.

• the integral does not converge at $x\to0$ – Santosh Linkha Nov 28 '13 at 7:35
• As far as I know, that formula for $f(x)/x$ is correct if $\lim_{x\to 0^+}(f/x)<\infty$. – mrs Nov 28 '13 at 8:40
• @SofiaJune: Are you sure it is not $\frac{1- \cos x}{x}$? – Amzoti Nov 28 '13 at 20:44