Question Detail
Question
Obtain the integral ∫log x dx
Correct Answer
Option B is the correct answer.
Detailed Explanation
To integrate ∫log x dx (assuming natural logarithm, ln x), we use integration by parts, ∫u dv = uv - ∫v du.Let u = ln x and dv = dx.Then du = (1/x) dx and v = x.∫ln x dx = x ln x - ∫x (1/x) dx= x ln x - ∫1 dx= x ln x - x + C= x(ln x - 1) + CThis matches option B.
Hint
Use integration by parts, setting u = ln x and dv = dx.