Evaluate : `int_(0)^(9) (1)/(1+sqrt(x))dx`

Explanation

To evaluate the integral \( I = \int_{0}^{9} \frac{1}{1+\sqrt{x}} \, dx \), we will use a substitution method.

### Step 1: Substitution
Let \( x = t^2 \). Then, we differentiate to find \( dx \):
\[ dx = 2t \, dt \]

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