Evaluate: `int_0^1sin^(-1)((2x)/(1+x^2))dx`

Explanation

To evaluate the integral \( I = \int_0^1 \sin^{-1}\left(\frac{2x}{1+x^2}\right)dx \), we can follow these steps:

### Step 1: Substitution
Let \( x = \tan(\theta) \). Then, \( dx = \sec^2(\theta) d\theta \) and the limits change as follows:
- When \( x = 0 \), \( \theta = 0 \).
- When \( x = 1 \), \( \theta = \frac{\pi}{4} \).

### Step 2: Rewrite the Integral
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