Question Detail

This integral is solved using integration by parts, where ∫ u dv = uv - ∫ v du. Let u = ln x (because its derivative simplifies) and dv = 1 dx. Then, du = (1⁄x) dx and v = ∫ 1 dx = x. Substitute these into the integration by parts formula: ∫ ln x dx = (ln x) * x - ∫ x * (1⁄x) dx. ∫ ln x dx = x ln x - ∫ 1 dx. The integral of 1 with respect to x is x. So, ∫ ln x dx = x ln x - x + C. This matches option C.