Evaluate: (i)`int_0^4 1/(x+sqrt(x))dx` (ii) `int_0^1(2x)/(5x^2+1)dx`

Explanation

Let's evaluate the given integrals step by step.

### Part (i): Evaluate \(\int_0^4 \frac{1}{x + \sqrt{x}} \, dx\)

1. **Substitution**: Let \(x = t^2\). Then, \(dx = 2t \, dt\).
2. **Change of Limits**:
- When \(x = 0\), \(t = 0\).
- When \(x = 4\), \(t = 2\).
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