Evaluate the Integral Using Integration by Parts $\int x e ^ { 3 x } d x$

Multiple Choice

Evaluate the integral using integration by parts.
- $\int x e ^ { 3 x } d x$

A) $\frac { 1 } { 6 }$ $x ^ { 2 }$ $e ^ { 3 x }$ + C
B) $e ^ { 3 x }$ $\left( \frac { 1 } { 3 } x - \frac { 1 } { 9 } \right)$ + C
C) $e ^ { 3 x }$ $\left( \frac { 1 } { 3 } x - 1 \right)$ + C
D) $\frac { 1 } { 3 }$ $e ^ { 3 x }$ + C