Evaluate : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx`

Explanation

To evaluate the integral \( I = \int_{0}^{1} \frac{x}{\sqrt{1+x^2}} \, dx \), we will use a substitution method. Here are the steps:

### Step 1: Substitution
Let \( t = 1 + x^2 \). Then, we differentiate both sides to find \( dx \):
\[ dt = 2x \, dx \quad \Rightarrow \quad dx = \frac{dt}{2x} \]
Now we also need to express \( x \) in terms of \( t \):
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