Evaluate ∫0111+x4dx\int_0^1 \frac{1}{1+x^4} dx∫011+x41dx.
142(ln(1+2+11−2+1)+2arctan(1+2)+2arctan(2−1))\frac{1}{4\sqrt{2}} (\ln(\frac{1+\sqrt{2}+1}{1-\sqrt{2}+1}) + 2\arctan(1+\sqrt{2}) + 2\arctan(\sqrt{2}-1))421(ln(1−2+11+2+1)+2arctan(1+2)+2arctan(2−1))
π22\frac{\pi}{2\sqrt{2}}22π
122ln(1+2)\frac{1}{2\sqrt{2}} \ln(1+\sqrt{2})221ln(1+2)
π4\frac{\pi}{4}4π