Which of the following is equivalent to ∫dxx4+1\int \frac{dx}{x^4+1}∫x4+1dx?
142ln∣x2+x2+1x2−x2+1∣+122(arctan(x2+1)+arctan(x2−1))\frac{1}{4\sqrt{2}} \ln|\frac{x^2+x\sqrt{2}+1}{x^2-x\sqrt{2}+1}| + \frac{1}{2\sqrt{2}} (\arctan(x\sqrt{2}+1) + \arctan(x\sqrt{2}-1))421ln∣x2−x2+1x2+x2+1∣+221(arctan(x2+1)+arctan(x2−1))
12arctan(x2)+C\frac{1}{2} \arctan(x^2) + C21arctan(x2)+C
12ln∣x4+1∣+C\frac{1}{\sqrt{2}} \ln|x^4+1| + C21ln∣x4+1∣+C
122(arctan(x2+1))\frac{1}{2\sqrt{2}} (\arctan(x^2+1))221(arctan(x2+1))