I want to integrate an equation but I am unable to understand how do I convert the d(1-c) term to some dx term. Please help me understand such manipulations and share any helpful resources to understand more about them. Equation
$\frac{d(1-c)}{dt}=-1.4\times 10^{-4} \times (1-c)^2(3-\frac{c}{2})$
$\int_1^\frac{1}{2} \frac{d(1-c)}{(1-c)^2(3-\frac{c}{2})}=-1.4\times 10^{-4} \int_0^t dt$
$\frac{d(1-c)}{dc}=-1\implies d(1-c)=-d(c)$.
Alternatively you can substitute $m=1-c$ and your LHS becomes$$\int_0^{1/2}\frac{2~dm}{m^2(5+m)}$$Integrate this with respect to $m$ and substitute $1-c$ back in the final result.