\[ \int \frac {x}{\left (-2+3 x^2\right ) \left (-1+3 x^2\right )^{3/4}} \, dx \]
Optimal antiderivative \[ -\frac {\arctan \! \left (\left (3 x^{2}-1\right )^{\frac {1}{4}}\right )}{3}-\frac {\arctanh \! \left (\left (3 x^{2}-1\right )^{\frac {1}{4}}\right )}{3} \]
command
integrate(x/(3*x**2-2)/(3*x**2-1)**(3/4),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \int \frac {x}{\left (3 x^{2} - 2\right ) \left (3 x^{2} - 1\right )^{\frac {3}{4}}}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\log {\left (\sqrt [4]{3 x^{2} - 1} - 1 \right )}}{6} - \frac {\log {\left (\sqrt [4]{3 x^{2} - 1} + 1 \right )}}{6} - \frac {\operatorname {atan}{\left (\sqrt [4]{3 x^{2} - 1} \right )}}{3} \]