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$\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x=$
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The correct answer is:
$2 \sqrt{x} e^{x}+c$
$\begin{aligned} I &=\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x \\ &=\int e^{x}\left(\frac{1}{\sqrt{x}}+2 \sqrt{x}\right) d x=\int e^{x}\left(2 \sqrt{x}+\frac{1}{\sqrt{x}}\right) d x=2 \int e^{x}\left(\sqrt{x}+\frac{1}{2 \sqrt{x}}\right) d x \\ &=2 e^{x} \sqrt{x}+c \end{aligned}$
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