\(\int x^{2}e^{2x}dx=\)
Answer & explanation
Correct answer: option 4
\(\begin{aligned}\int x^{2}e^{2x}dx&=\frac{x^2 e^{2x}}{2}-\int 2x \frac{e^{2x}}{2}dx\\ &=\frac{x^2 e^{2x}}{2}-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}\end{aligned}\)
Correct answer: option 4