Solving $dx/dt=0.2x^2left(1-x/3right)$ for the initial condition $x(0)=x_0$

I am trying to solve the system $$frac{dx}{dt}=0.2x^2left(1-frac{x}{3}right),$$ if $x(0)=x_0$. This is a separable ODE, and my attempt is below.
begin{align}
frac{dx}{dt}&=0.2x^2left(1-frac{x}{3}right) \
intfrac{dx}{x^2(3-x)}&=frac{1}{15}int dt \
int frac{1/9}{x}+frac{1/3}{x^2}+frac{1/3}{3-x} dx&=frac{1}{15}int dt \
frac{1}{9}ln(x)-frac{1}{3x}-frac{1}{3}ln(3-x)&=frac{t}{15} +C, Cinmathbb{R}.
end{align}
However, I am unsure of how to proceed.