Find ∫1x3+1 dx\int \frac{1}{x^3+1} \, dx∫x3+11dx.
16ln∣(x+1)2x2−x+1∣+13arctan(2x−13)+C\frac{1}{6} \ln|\frac{(x+1)^2}{x^2-x+1}| + \frac{1}{\sqrt{3}} \arctan(\frac{2x-1}{\sqrt{3}}) + C61ln∣x2−x+1(x+1)2∣+31arctan(32x−1)+C
13ln∣x+1∣−16ln∣x2−x+1∣+13arctan(2x−13)+C\frac{1}{3} \ln|x+1| - \frac{1}{6} \ln|x^2-x+1| + \frac{1}{\sqrt{3}} \arctan(\frac{2x-1}{\sqrt{3}}) + C31ln∣x+1∣−61ln∣x2−x+1∣+31arctan(32x−1)+C
13ln∣x+1∣+16ln∣x2−x+1∣+13arctan(2x−13)+C\frac{1}{3} \ln|x+1| + \frac{1}{6} \ln|x^2-x+1| + \frac{1}{\sqrt{3}} \arctan(\frac{2x-1}{\sqrt{3}}) + C31ln∣x+1∣+61ln∣x2−x+1∣+31arctan(32x−1)+C
ln∣x3+1∣+C\ln|x^3+1| + Cln∣x3+1∣+C