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

Explanation

To evaluate the integral \( I = \int_0^1 \frac{\tan^{-1} x}{1+x^2} \, dx \), we will use substitution.

### Step 1: Substitution
Let \( t = \tan^{-1} x \). Then, we differentiate both sides:
\[ dt = \frac{1}{1+x^2} \, dx \quad \Rightarrow \quad dx = (1+x^2) \, dt \]
We also need to change the limits of integration. When \( x = 0 \), \( t = \tan^{-1}(0) = 0 \). When \( x = 1 \), \( t = \tan^{-1}(1) = \frac{\pi}{4} \).
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