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To evaluate the integral

\[
\int_1^1 \sqrt{\frac{1+x}{1-x}} \, dx
\]

let's analyze it step by step.

### 1. Check the Limits of Integration

The integral is given with limits from \(1\) to \(1\). Since the limits of integration are the same, the integral evaluates to zero regardless of the integrand. This is a general property of definite integrals:

\[
\int_a^a f(x) \, dx = 0
\]

Therefore, the value of the integral is:

\[
\boxed{0}
\]

This conclusion is independent of the complexity of the integrand since the

Evaluate the integral \( \int_1^1 \sqrt{\frac{1+x}{1-x}} \, dx \).

Explore how to evaluate the definite integral \( \int_1^1 \sqrt{\frac{1+x}{1-x}} \, dx \) and understand why the integral is zero due to the property of definite integrals with equal limits. This problem is suitable for undergraduate calculus students.

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