Find ∫dxx4+1\int \frac{dx}{x^4+1}∫x4+1dx.
142ln∣x2+x2+1x2−x2+1∣+122arctan(x21−x2)+C\frac{1}{4\sqrt{2}} \ln \left| \frac{x^2+x\sqrt{2}+1}{x^2-x\sqrt{2}+1} \right| + \frac{1}{2\sqrt{2}} \arctan \left( \frac{x\sqrt{2}}{1-x^2} \right) + C421lnx2−x2+1x2+x2+1+221arctan(1−x2x2)+C
142ln∣x2−x2+1x2+x2+1∣+122arctan(x21−x2)+C\frac{1}{4\sqrt{2}} \ln \left| \frac{x^2-x\sqrt{2}+1}{x^2+x\sqrt{2}+1} \right| + \frac{1}{2\sqrt{2}} \arctan \left( \frac{x\sqrt{2}}{1-x^2} \right) + C421lnx2+x2+1x2−x2+1+221arctan(1−x2x2)+C
122ln∣x2+x2+1x2−x2+1∣+C\frac{1}{2\sqrt{2}} \ln \left| \frac{x^2+x\sqrt{2}+1}{x^2-x\sqrt{2}+1} \right| + C221lnx2−x2+1x2+x2+1+C
arctan(x2)+C\arctan(x^2) + Carctan(x2)+C