Evaluate the Integral $$\int \mathrm { e } ^ { 2 x } \mathrm { x } ^ { 2 } \mathrm { dx }$$

question 31

Multiple Choice

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

• A) \(\frac { 1 } { 2 } x ^ { 2 } e ^ { 2 x } - \frac { 1 } { 4 } x e ^ { 2 x } + \frac { 1 } { 4 } e ^ { 2 x } + C\)
• B) \(\frac { 1 } { 2 } \mathrm { x } ^ { 2 } \mathrm { e } ^ { 2 \mathrm { x } } - \frac { 1 } { 2 } \mathrm { xe } ^{2 \mathrm { x } }+ \frac { 1 } { 4 } \mathrm { e } ^ { 2 \mathrm { x } } + \mathrm { C }\)
• C) \(\frac { 1 } { 2 } \mathrm { x } ^ { 2 } \mathrm { e } ^ { 2 \mathrm { x } } - \frac { 1 } { 2 } \mathrm { xe } ^ { 2 \mathrm { x } } + \mathrm { C }\)
• D) \(\frac { 1 } { 2 } x ^ { 2 } e ^ { 2 x } - x e ^ { 2 x } + \frac { 1 } { 4 } e ^ { 2 x } + C\)

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