Find ∫dxx4+x2+1\int \frac{dx}{x^4+x^2+1}∫x4+x2+1dx.
123ln∣x2+x3+1x2−x3+1∣+13arctan(2x2+13)\frac{1}{2\sqrt{3}} \ln | \frac{x^2+x\sqrt{3}+1}{x^2-x\sqrt{3}+1} | + \frac{1}{\sqrt{3}} \arctan(\frac{2x^2+1}{\sqrt{3}})231ln∣x2−x3+1x2+x3+1∣+31arctan(32x2+1)
143ln∣x2+x3+1x2−x3+1∣+123arctan(2x3−x2)\frac{1}{4\sqrt{3}} \ln | \frac{x^2+x\sqrt{3}+1}{x^2-x\sqrt{3}+1} | + \frac{1}{2\sqrt{3}} \arctan(\frac{2x}{\sqrt{3}-x^2})431ln∣x2−x3+1x2+x3+1∣+231arctan(3−x22x)
arctan(x2)\arctan(x^2)arctan(x2)
ln(x2+1)\ln(x^2+1)ln(x2+1)