How to compute $\int_0^1 \frac{1}{1+x^4}\;dx$? I am having problems trying to compute $$\int_0^1 \frac{1}{1+x^4}\;dx$$
Wolfram alpha gives an answer $$\frac{\pi + 2 \coth^{-1}(\sqrt{2})}{4 \sqrt{2}}$$

Factor as $x^4+1=x^4+2x^2+1-2x^2=(x^2+1)^2-(\sqrt 2 \cdot x)^2=(x^2+\sqrt 2 x+1)(x^2-\sqrt 2 x +1)$ and use partial fractions.
