Answer
$\dfrac{C}{s}$
Work Step by Step
The Laplace Transform of $f(x)$ can be found as:
$L f(s)=\int_0^{\infty} C e^{-sx}\ dx\\=\lim\limits_{R \to \infty}[\dfrac{-C}{s}e^{-sx}]_0^R\\=\lim\limits_{R \to \infty}\dfrac{-C}{s}(e^{-sR}-1)\\=\dfrac{-C}{s} (0-1)\\=\dfrac{C}{s}$
