\[ \int \frac {\sqrt {1-x^6} \left (1+2 x^6\right ) \left (1+x^2-x^4-2 x^6-x^8+x^{12}\right )}{\left (-1+x^6\right ) \left (-1+2 x^6-3 x^{12}+x^{18}\right )} \, dx \]
Optimal antiderivative \[ -\frac {\arctan \left (\frac {x}{\sqrt {-x^{6}+1}}\right )}{3}-\frac {\arctan \left (\frac {x \sqrt {-x^{6}+1}}{x^{6}+x^{2}-1}\right )}{3}-\frac {\arctanh \left (\frac {\sqrt {3}\, x \sqrt {-x^{6}+1}}{x^{6}-x^{2}-1}\right ) \sqrt {3}}{3} \]
command
int((-x^6+1)^(1/2)*(2*x^6+1)*(x^12-x^8-2*x^6-x^4+x^2+1)/(x^6-1)/(x^18-3*x^12+2*x^6-1),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| trager | \(\text {Expression too large to display}\) | \(1681\) |
Maple 2021.1 output
\[\int \frac {\sqrt {-x^{6}+1}\, \left (2 x^{6}+1\right ) \left (x^{12}-x^{8}-2 x^{6}-x^{4}+x^{2}+1\right )}{\left (x^{6}-1\right ) \left (x^{18}-3 x^{12}+2 x^{6}-1\right )}\, dx\]________________________________________________________________________________________