## Calculus 8th Edition

$\int_{1}^{\infty}\frac{x}{x^{4}+1}=\lim\limits_{t \to \infty}\int_{1}^{\infty} \frac{x}{x^{4}+1}=\lim\limits_{t \to \infty}[\frac{1}{2}tan^{-1}(x^{2})]^{t}_{1}=\frac{1}{2}[tan^{-1}(\infty)-tan^{-1}(1)]=\frac{1}{2}[\frac{\pi}{2}-\frac{\pi}{4}]$ $=\frac{\pi}{8}$ Hence, the given series is convergent.