Question Detail
Question
Evaluate the integral ∫xex dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
This integral requires integration by parts, which states ∫u dv = uv - ∫v du.Let u = x, so du = dx.Let dv = ex dx, so v = ex.Applying the formula: ∫xex dx = xex - ∫ex dx = xex - ex + C.Factoring out ex gives ex(x - 1) + C.
Hint
Use integration by parts with u=x and dv=ex dx.