∫ f'(x)/f(x) dx = ln(x) + c
therefore to make it represent the form ∫ f'(x)/f(x) dx
do: -∫ f'(x)/f(x) dx = -∫ -1/(1-x)dx = -ln(1-x) + c
you could use the variable u (substitution) if you like:
u=(1-x)
du/dx = -1
∫ (1/u)(-1) du = -∫ (1/u) du = -ln(u) + c = -ln(1-x) + c