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, which states ∫ u dv = uv - ∫ v du.Let u = ln x and dv = dx.Then, we find du and v:du = d/dx (ln x) dx = (1/x) dxv = ∫ dx = xSubstitute 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.This matches option C.
Hint
Use integration by parts. A common trick for integrating ln x is to let u = ln x and dv = dx.