Question Detail
Question
Find ∫2x/(x+1) dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To integrate ∫2x/(x+1) dx, we can perform polynomial division or algebraic manipulation.2x / (x+1) = (2(x+1) - 2) / (x+1) = 2 - 2/(x+1)Now integrate term by term:∫(2 - 2/(x+1)) dx = ∫2 dx - ∫2/(x+1) dx= 2x - 2 ln|x+1| + CFactor out 2:= 2(x - ln|x+1|) + CThis matches option D.
Hint
Simplify the integrand by dividing the numerator by the denominator, or by rewriting the numerator in terms of (x+1).