Question Detail
Question
Integrate ∫ x eˣ dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
This integral requires integration by parts, using the formula ∫ u dv = uv - ∫ v du.Let u = x and dv = eˣ dx.Then, du = dx and v = ∫ eˣ dx = eˣ.Applying the formula:∫ x eˣ dx = x * eˣ - ∫ eˣ dx= x eˣ - eˣ + CFactor out eˣ: = (x - 1)eˣ + C.
Hint
This is a classic integration by parts problem. Choose 'u' and 'dv' carefully.