Find ∫1x4+1dx\int \frac{1}{x^4+1} dx∫x4+11dx.
142ln∣x2+x2+1x2−x2+1∣+122arctan(x21−x2)+C\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(\frac{x\sqrt{2}}{1-x^2}) + C421ln∣x2−x2+1x2+x2+1∣+221arctan(1−x2x2)+C
142ln∣x2−x2+1x2+x2+1∣+122arctan(x21+x2)+C\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(\frac{x\sqrt{2}}{1+x^2}) + C421ln∣x2+x2+1x2−x2+1∣+221arctan(1+x2x2)+C
12arctan(x2)+C\frac{1}{\sqrt{2}} \arctan(x^2) + C21arctan(x2)+C
None of these