A) \[(3x-1)/4\]
B) \[(2x+1)/2\]
C) \[(2x-1)/4\]
D) \[(x-4)/6\]
Correct Answer: C
Solution :
\[\int{x{{e}^{2x}}dx=\frac{x{{e}^{2x}}}{2}}-\int{1.\,\frac{{{e}^{2x}}}{2}dx}\]\[=\frac{x{{e}^{2x}}}{2}-\frac{{{e}^{2x}}}{4}+c\] \[={{e}^{2x}}\left( \frac{2x-1}{4} \right)+c\] Þ \[f(x)=\frac{(2x-1)}{4}.\]You need to login to perform this action.
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