Evaluate $\int \frac{x}{x^{4} + 1}\,dx$.

Explanation

1. 01

   Put $t = x^{2}$, $dt = 2x\,dx$: $\frac{1}{2}\int \frac{dt}{t^{2} + 1}$.

2. 02

   $= \frac{1}{2}\tan^{-1} t = \frac{1}{2}\tan^{-1} x^{2} + C$.