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.

$$x(t) \rightleftharpoons X(s)$$
$$tx(t) \rightleftharpoons -\frac{dX(s)}{ds}$$
$$x_1(t) \rightleftharpoons ln(s)$$
$$tx_1(t) \rightleftharpoons -\frac{1}{s}$$
$$tx_1(t) = -u(t)$$
$$x_1(t) = -\frac{u(t)}{t}$$
$$x_2(t) \rightleftharpoons \frac{1}{(s+2)^2}$$
$$e^{-2t} u(t) \rightleftharpoons \frac{1}{s+2}$$
$$te^{-2t} u(t) \rightleftharpoons \frac{1}{(s+2)^2}$$
$$x_2(t) = te^{-2t}u(t)$$
$$x_1(t)*x_2(t) \rightleftharpoons X_1(s) X_2(s)$$
$$-\frac{u(t)}{t} * te^{-2t}u(t) \rightleftharpoons \frac{ln(s)}{(s+2)^2}$$
