Evaluate the Integral Using Integration by Parts $\int x \mathrm { e } ^ { - x } \mathrm { dx }$

Evaluate the integral using integration by parts.
- $\int x \mathrm { e } ^ { - x } \mathrm { dx }$

A) - x $\mathrm { e } ^ { - \mathrm { x } }$ - $\mathrm { e } ^ { - \mathrm { x } }$ + C
B) - x $\mathrm { e } ^ { - \mathrm { x } }$ + $\mathrm { e } ^ { - \mathrm { x } }$ + C
C) x $\mathrm { e } ^ { - \mathrm { x } }$ + $\mathrm { e } ^ { - \mathrm { x } }$ + C
D) x $\mathrm { e } ^ { - \mathrm { x } }$ - $\mathrm { e } ^ { - \mathrm { x } }$ + C

Correct Answer:

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