Evaluate ∫011x4+1dx\int_0^1 \frac{1}{x^4+1} dx∫01x4+11dx.
142ln(1+2+x21−2+x2)+122(arctan(1+2x)+arctan(2x−1))\frac{1}{4\sqrt{2}} \ln(\frac{1+\sqrt{2}+x^2}{1-\sqrt{2}+x^2}) + \frac{1}{2\sqrt{2}}(\arctan(1+\sqrt{2}x) + \arctan(\sqrt{2}x-1))421ln(1−2+x21+2+x2)+221(arctan(1+2x)+arctan(2x−1))
π4\frac{\pi}{4}4π
122ln(2+1)\frac{1}{2\sqrt{2}} \ln(\sqrt{2}+1)221ln(2+1)
π22\frac{\pi}{2\sqrt{2}}22π