Question Detail

To solve ∫ln(x/2) dx, use integration by parts, which states ∫u dv = uv - ∫v du.Let u = ln(x/2) and dv = dx.Then, du = d/dx(ln(x/2)) dx = (1/(x/2)) * (1/2) dx = (2/x) * (1/2) dx = 1/x dx.And v = ∫dv = ∫dx = x.Substitute these into the integration by parts formula:∫ln(x/2) dx = x ln(x/2) - ∫x (1/x) dx= x ln(x/2) - ∫1 dx= x ln(x/2) - x + C= x (ln(x/2) - 1) + C.This matches option D.