[2] \( \int\left(4 \sqrt{x}+\frac{8}{\sqrt{x}}\right) d x \)

Step 1 ：\(\int\left(4 \sqrt{x}+\frac{8}{\sqrt{x}}\right) dx = \int(4x^{\frac{1}{2}}+8x^{-\frac{1}{2}}) dx\)

Step 2 ：\(= 4\int x^{\frac{1}{2}} dx + 8\int x^{-\frac{1}{2}} dx\)

Step 3 ：\(= 4\left(\frac{2}{3}x^{\frac{3}{2}}\right) + 8\left(2x^{\frac{1}{2}}\right) + C\)

Step 4 ：\(= \frac{8}{3}x^{\frac{3}{2}} + 16\sqrt{x} + C\)