$\displaystyle \frac{dy}{dx} = x(1-x) $

$\displaystyle dy = x(1-x) dx $

$\displaystyle dy = x-x^{2} dx $

$\displaystyle \int dy = \int x-x^{2} dx $

is this so far correct? cuse my book gives me a solution like this $\displaystyle \int \frac{1}{x(1-x)} = \int dy $

And i have no idea how they got this?