\[ \int \frac {\left (-1+x^6\right ) \left (1+x^6\right )^{2/3}}{x^3 \left (2-x^3+2 x^6\right )} \, dx \]
Optimal antiderivative \[ \frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4 x^{2}}-\frac {\arctan \left (\frac {\sqrt {3}\, x}{x +2 \,2^{\frac {1}{3}} \left (x^{6}+1\right )^{\frac {1}{3}}}\right ) 2^{\frac {1}{3}} \sqrt {3}}{12}+\frac {\ln \left (-x +2^{\frac {1}{3}} \left (x^{6}+1\right )^{\frac {1}{3}}\right ) 2^{\frac {1}{3}}}{12}-\frac {\ln \left (x^{2}+2^{\frac {1}{3}} x \left (x^{6}+1\right )^{\frac {1}{3}}+2^{\frac {2}{3}} \left (x^{6}+1\right )^{\frac {2}{3}}\right ) 2^{\frac {1}{3}}}{24} \]
command
int((x^6-1)*(x^6+1)^(2/3)/x^3/(2*x^6-x^3+2),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| trager | \(\text {Expression too large to display}\) | \(1475\) |
Maple 2021.1 output
\[\int \frac {\left (x^{6}-1\right ) \left (x^{6}+1\right )^{\frac {2}{3}}}{x^{3} \left (2 x^{6}-x^{3}+2\right )}\, dx\]________________________________________________________________________________________