Evaluate $\int_{0}^{1} \frac{2 x}{x^{2} + 1}\,dx$.

Explanation

1. 01

   An antiderivative is $F(x) = \log{\left(x^{2} + 1 \right)}$.

2. 02

   By the fundamental theorem, the integral is $F(1) - F(0) = \log 2$.