# What is the general form of a logistic function?

$x ' \left(t\right) = k \cdot x \left(t\right) \cdot \left(a - x \left(t\right)\right)$ then you put it like this to apply integral calculus
$k = \frac{x ' \left(t\right)}{x \cdot \left(a - x \left(t\right)\right)}$
int_(tº)^tk*dt=int_(xº)^xdx/(x*(a-x))