Evaluate the following integral: `int_0^1cos^(-1)((1-x^2)/(1+x^2))dx`

Explanation

To evaluate the integral \( I = \int_0^1 \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right) dx \), we will follow a step-by-step approach.

### Step 1: Change of Variable
We will use the substitution \( x = \tan(t) \). Then, the differential \( dx \) becomes:
\[ dx = \sec^2(t) dt \]
Also, we need to change the limits of integration. When \( x = 0 \), \( t = 0 \) and when \( x = 1 \), \( t = \frac{\pi}{4} \).
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