Laplace Transform of Natural Logarithm

Theorem

 * $\laptrans {\ln t} = \dfrac {\map {\Gamma'} 1 - \ln s} s = -\dfrac {\gamma + \ln s} s$

where:
 * $\laptrans f$ denotes the Laplace transform of the function $f$
 * $\Gamma$ denotes the Gamma function
 * $\gamma$ denotes the Euler-Mascheroni constant.