Difficult Inverse Laplace Transform I've had this question in my exam, which most of my batch mates couldn't solve it.The question by the way is the Laplace Transform inverse of  
$$\frac{\ln s}{(s+1)^2}$$
A Hint was also given, which includes the Laplace Transform of ln t.

$f(s,a) = L(t^a) = \frac{\Gamma(a+1)}{s^{a+1}} $  
Differentiating with respect to a, we get
$L(t^a\cdot lnt) = \frac{\Gamma'(a+1) - \Gamma(a+1)\cdot lns}{s^{a+1}} $
set a = 1.
