\[ \int \frac {1-x+x^2}{\left (-1+x^2\right ) \sqrt [3]{x^2+x^4}} \, dx \]
Optimal antiderivative \[ -\frac {3 \sqrt {3}\, \arctan \! \left (\frac {\sqrt {3}\, x}{-x +2^{\frac {2}{3}} \left (x^{4}+x^{2}\right )^{\frac {1}{3}}}\right ) 2^{\frac {2}{3}}}{8}-\frac {\sqrt {3}\, \arctan \! \left (\frac {\sqrt {3}\, x}{x +2^{\frac {2}{3}} \left (x^{4}+x^{2}\right )^{\frac {1}{3}}}\right ) 2^{\frac {2}{3}}}{8}+\frac {\ln \! \left (-2 x +2^{\frac {2}{3}} \left (x^{4}+x^{2}\right )^{\frac {1}{3}}\right ) 2^{\frac {2}{3}}}{8}-\frac {3 \ln \! \left (2 x +2^{\frac {2}{3}} \left (x^{4}+x^{2}\right )^{\frac {1}{3}}\right ) 2^{\frac {2}{3}}}{8}+\frac {3 \ln \! \left (-2 x^{2}+2^{\frac {2}{3}} x \left (x^{4}+x^{2}\right )^{\frac {1}{3}}-2^{\frac {1}{3}} \left (x^{4}+x^{2}\right )^{\frac {2}{3}}\right ) 2^{\frac {2}{3}}}{16}-\frac {\ln \! \left (2 x^{2}+2^{\frac {2}{3}} x \left (x^{4}+x^{2}\right )^{\frac {1}{3}}+2^{\frac {1}{3}} \left (x^{4}+x^{2}\right )^{\frac {2}{3}}\right ) 2^{\frac {2}{3}}}{16} \]
command
int((x^2-x+1)/(x^2-1)/(x^4+x^2)^(1/3),x)
Maple 2022.1 output
\[\int \frac {x^{2}-x +1}{\left (x^{2}-1\right ) \left (x^{4}+x^{2}\right )^{\frac {1}{3}}}\, dx\]
Maple 2021.1 output
| method | result | size |
| trager | \(\text {Expression too large to display}\) | \(8780\) |