Evaluate the Integral Using Integration by Parts $\int x ^ { 2 }$

Evaluate the integral using integration by parts.
- $\int x ^ { 2 }$ $\mathrm { e } ^ { 2 x }$ dx

A) $\mathrm { e } ^ { 2 x }$ $\left( \frac { x ^ { 2 } - x } { 2 } \right)$ + 1 + C
B) $\mathrm { e } ^ { 2 x }$ $\left( \frac { x ^ { 2 } - 4 x } { 2 } \right)$ + C
C) $\mathrm { e } ^ { 2 x }$ $\left( \frac { x ^ { 2 } - 2 x } { 2 } \right)$ + C
D) $\mathrm { e } ^ { 2 x }$ $\left( \frac { 2 x ^ { 2 } - 2 x + 1 } { 4 } \right)$ + C

Correct Answer:

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