Evaluate:
(i) `int(x^(-1//3)+sqrt(x)+2)/(x^3)\ dx`
(ii) `int((1+sqrt(x))^2)/(sqrt(x))\ dx`

Explanation

To evaluate the given integrals, we will break them down step by step.

### Part (i): Evaluate \( \int \frac{x^{-\frac{1}{3}} + \sqrt{x} + 2}{x^3} \, dx \)

1. **Rewrite the integrand**:
\[ \frac{x^{-\frac{1}{3}} + \sqrt{x} + 2}{x^3} = \frac{x^{-\frac{1}{3}}}{x^3} + \frac{\sqrt{x}}{x^3} + \frac{2}{x^3} = x^{-\frac{1}{3} - 3} + x^{\frac{1}{2} - 3} + 2x^{-3} \]
...