Evaluate $\int x e^{x}\, dx$

Question

Accepted Answer

$x e^{x} - e^{x} + C$. Using integration by parts with u = x and dv = eˣ dx: du = dx, v = eˣ. So ∫xeˣ dx = xeˣ - ∫eˣ dx = xeˣ - eˣ + C = eˣ(x-1) + C. Note that options B and C are equivalent, so checking: B = xeˣ - eˣ + C and C = eˣ(x-1) + C = xeˣ - eˣ + C, making both B and C correct. The intended distinct correct answer

Answer

A) $x e^{x} + e^{x} + C$

Answer

B) $x e^{x} - e^{x} + C$

Answer

C) $e^{x}(x-1) + C$

Answer

D) $\frac{x^2}{2}e^{x} + C$

Evaluate $\int x e^{x}\, dx$

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