Question Detail
Question
Integrate ∫x eˣ 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 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 + C= eˣ(x - 1) + C.
Hint
Remember the integration by parts formula: ∫u dv = uv - ∫v du. Choose u and dv carefully (LIATE rule can help).