The power of 2

Algebra Level 3

$\left(1 - x^{32}\right)\left(\frac{1}{1 - x} + \frac{1}{x + 1} + \frac{2}{x^2 + 1} + \frac{4}{1 + x^4} + \frac{8}{1 + x^8} + \frac{16}{1 + x^{16}}\right) = ?$

This is part of the series: It's easy, believe me!