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| \(\int x^{2}e^{2x}dx=\) |
\(e^{2x}[2x^2-2x+1]+c\) \(\frac{1}{2}e^{2x}[2x^2-2x+1]\) \(\frac{1}{4}e^{2x}[2x^2+2x+1]\) None of these |
| None of these |
| \(\begin{aligned}\int x^{2}e^{2x}dx&=\frac{x^2 e^{2x}}{2}-\int 2x \frac{e^{2x}}{2}dx\\ &=\frac{x^2 e^{2x}}{2}-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}\end{aligned}\) |
