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The integral from 0 to pi of dx / (1 - 2*a*cos(x) + a²), where a < 1, is equal to:

1. pi * a * log(2) / 4
2. 4*pi / (2 - a²)
3. pi / (1 - a²)
4. None of these

Correct answer: pi / (1 - a²)

Solution

This is a standard definite integral. Using the Weierstrass substitution t = tan(x/2): the integral evaluates to pi/(1-a²) for |a| < 1. This is a well-known result from Fourier analysis and complex residues.

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