Question Detail
Question
Integrate ∫ xeˣ dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
This integral requires integration by parts, formula: ∫ u dv = uv - ∫ v du.Let u = x, so du = dx.Let dv = eˣ dx, so v = ∫ eˣ dx = eˣ.Substitute these into the integration by parts formula:∫ xeˣ dx = x * eˣ - ∫ eˣ dx= xeˣ - eˣ + C= eˣ(x - 1) + C.This matches option D.
Hint
Apply integration by parts. Choose u = x and dv = eˣ dx.