Question Detail
Question
Simplify ∫ ln x dx
Correct Answer
Option C is the correct answer.
Detailed Explanation
This integral requires integration by parts: ∫ u dv = uv - ∫ v du.Choose u = ln x and dv = dx.Then, du = (1/x) dx and v = x.Substitute these into the integration by parts formula:∫ ln x dx = (ln x) * (x) - ∫ (x) * (1/x) dx= x ln x - ∫ 1 dx= x ln x - x + C.
Hint
This is a classic integral that requires integration by parts. Think about which part to choose as 'u' and which as 'dv'.