$\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x=$

Question

Aicharya · Accepted Answer

$\begin{aligned} I &=\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x \ &=\int e^{x}\left(\frac{1}{\sqrt{x}}+2 \sqrt{x}ight) d x=\int e^{x}\left(2 \sqrt{x}+\frac{1}{\sqrt{x}}ight) d x=2 \int e^{x}\left(\sqrt{x}+\frac{1}{2 \sqrt{x}}ight) d x \ &=2 e^{x} \sqrt{x}+c \end{aligned}$

$\int \frac{e^{x}}{\sqrt{x}}(1+2 x) d x=$

Solution