∫ dx/(4x - x^2)
= ∫ dx/[x(4 - x)]
= (1/4)∫ [(4 - x) + x]/[x/(4 - x)] dx
= (1/4)∫ [1/x + 1/(4 - x)] dx
= (1/4)[ln(x) - ln(4 - x)] + C
= (1/4)ln[x/(4 - x)] + C