Question Detail
Question
Obtain the integral ∫log xdx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
Use integration by parts: ∫ u dv = uv - ∫ v du.Let u = log x (assuming natural logarithm, ln x) and dv = dx.Then du = (1/x) dx and v = x.∫ log x dx = x log x - ∫ x (1/x) dx= x log x - ∫ 1 dx= x log x - x + C= x (log x - 1) + C.This matches option B.
Hint
Apply integration by parts. Choose u = log x and dv = dx. Remember that d/dx (log x) = 1/x (for natural log).