MTH102 TMA3 Questions and Solutions : Evaluate \[\int x^{2} e^{3x} dx\]

Evaluate \[\int x^{2} e^{3x} dx\]
a) \[\frac{e^{3x}}{3}\left(x^{2}-\frac{2x}{3}+\frac{2}{9}\right)+c\]
b) \[-\frac{e^{3x}}{3}\left(x^{2}+\frac{2x}{3}-\frac{2}{9}\right)+c\]
c) \[\frac{e^{2x}}{3}\left(x^{3}-\frac{x}{4}+\frac{2}{9}\right)+c\]
d) \[\frac{e^{x}}{3}\left(x^{2}+\frac{2x}{3}-\frac{2}{5}\right)+c\]

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