∫ x eˣ dx (using integration by parts):
Ax² eˣ/2 + C
Bx² eˣ + C
Cx eˣ + C
D(x - 1) eˣ + C
Answer & Solution
Correct answer: D. (x - 1) eˣ + C
By parts: u = x, dv = eˣ dx, du = dx, v = eˣ. ∫ u dv = uv - ∫ v du = x eˣ - ∫ eˣ dx = x eˣ - eˣ + C = (x-1) eˣ + C.
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