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.To integrate ln x, we choose u = ln x and dv = dx.Then, differentiate u to find du: du = (1/x) dx.And integrate dv to find v: v = ∫ dx = x.Substitute these into the integration by parts formula:∫ ln x dx = (ln x) ∙ x - ∫ x ∙ (1/x) dx= x ln x - ∫ 1 dx.Now, integrate ∫ 1 dx = x.So, ∫ ln x dx = x ln x - x + C. This matches option C.
Hint
When integrating ln x, use integration by parts. A common strategy is to set u = ln x and dv = dx.