Question Detail
Question
Integrate ∫x/(x-1) dx
Correct Answer
Option B is the correct answer.
Detailed Explanation
To integrate x/(x-1), we can perform algebraic manipulation on the integrand.Add and subtract 1 in the numerator:x/(x-1) = (x-1) + 1/(x-1)Separate the terms:= (x-1)/(x-1) + 1/(x-1)= 1 + 1/(x-1)Now, integrate the simplified expression:∫(1 + 1/(x-1)) dx = ∫1 dx + ∫1/(x-1) dx= x + ln|x-1| + C. This matches option B.
Hint
Rewrite the integrand using algebraic manipulation to simplify it before integration. For example, add and subtract a term in the numerator to create a form that can be easily split.