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

$2 x \sqrt{x}+3 x+C$ (Here C is an arbitrary constant) $2 \sqrt{x}+C$ (Here C is an arbitrary constant) $x \sqrt{x}+x+C$ (Here C is an arbitrary constant) $\frac{x \sqrt{x}}{3}+\frac{x}{2}+C$ (Here C is an arbitrary constant)

$\frac{x \sqrt{x}}{3}+\frac{x}{2}+C$ (Here C is an arbitrary constant)

The correct answer is Option (4) - $\frac{x \sqrt{x}}{3}+\frac{x}{2}+C$ (Here C is an arbitrary constant)