Originally Posted by
o_O For a first-order reaction, the differential rate is given by: $\displaystyle r = -\frac{d[A]}{dt} = k[A]$
To get its integrated form, separate the variables:
$\displaystyle \begin{aligned}-\frac{d[A]}{[A]} & = k dt \\ -{\color{red}\int}\frac{d[A]}{[A]} & = {\color{red}\int} k dt \\ \ln [A] & = -kt + C\end{aligned}$
Normally, we're given an initial concentration, i.e. $\displaystyle [A]_0 \ \ @ \ \ t=0$
This enables us to solve for the constant: $\displaystyle \ln [A]_0 = -k(0) + C \ \Leftrightarrow \ C = \ln [A]_0$
I'm sure you can take it from here.