alleryUsing integration by parts, $\displaystyle\int x e^x\,dx$ equals:
A$(x + 1) e^x + C$
B$\dfrac{x^2}{2} e^x + C$
C$(x - 1) e^x + C$
D$x e^x + C$
Answer & Solution
Correct answer: C. $(x - 1) e^x + C$
Take $u = x$ (algebraic) and $dv = e^x\,dx$, then $du = dx$ and $v = e^x$.
**By parts:** $\int x e^x\,dx = x e^x - \int e^x\,dx = x e^x - e^x + C = (x - 1) e^x + C$.
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