Question Detail
Question
Simplify ∫ ln x dx
Correct Answer
Option C is the correct answer.
Detailed Explanation
To simplify ∫ ln x dx, we use integration by parts: ∫ u dv = uv - ∫ v du.Let u = ln x, so du = (1/x) dx.Let dv = dx, so 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 + CTherefore, the correct option is C.
Hint
Use integration by parts. A common choice for 'u' when integrating logarithms is the logarithm itself.